 Show Anyone who takes out a loan has to think about the cost of doing so. If you need to borrow money to finance a home purchase or a renovation, you’ll want your interest rate to be as low as possible. From an investors’ standpoint, however, higher interest rates present the opportunity to earn higher rates of return. Interest can be simple or it can compound over time. Don’t understand the difference between simple and compound interest? We’ll define both concepts and give plenty of examples. Do you have questions about how to optimize your finances? Speak to a financial advisor today. What Is Simple Interest?The term interest indicates how much you can earn from the money you originally invest. As your investment sits in an account over time, interest accumulates and you can watch your funds grow. To calculate the amount of simple interest you stand to earn as an investor, you can use the following formula: Principal Balance x Interest Rate. You can then multiply the product by the number of years you’re investing your money to find out what your return rate would look like over time. For example, if you decide to invest $2,000 in a money market account with a simple interest rate of 8.5%, you’ll earn $170 in interest after one year ($2,000 x 0.085). After five years, you’ll earn $850 (170 x 5) in interest. What Is Compound Interest?Compound interest represents the amount you earn from your initial investment in addition to the interest you earn – on top of the interest that has already accrued. You can calculate compound interest using the formula, A=P(1+r/n)nt. A is the amount you have after compounding. The value P is the principal balance. The value r is the interest rate (expressed as a decimal), n is the number of times that interest compounds per year and t is the number of years. Interest can compound either frequently (daily or monthly) or infrequently (quarterly, once a year or biannually). The more often your interest compounds, the more interest you’ll earn on your investment. It’s easy to see that money grows more quickly when it’s earning compound interest than when it’s earning simple interest. To return to the example above, if you invest $2,000 at an interest rate of 8.5% compounding twice a year for 5 years, your end balance will be $3,032.43. You will have earned $1,032.43 in interest, compared to $850 in the simple interest example. But if that same investment compounds monthly (12 times a year) instead of twice a year, you’ll end up with a balance of $3,054.60. As you can see, the frequency of compounding makes a difference in terms of your overall return rate. If you want to take advantage of compound interest, it’s a good idea to find out how often your interest will compound before you invest your money. Simple Interest vs. Compound Interest: What’s the Difference?Compared to compound interest, simple interest is easier to calculate and easier to understand. If you have a temporary loan or one with interest that doesn’t compound, you’ll only have to worry about interest added onto the outstanding principal balance. With mortgages and most car loans, for example, simple interest accrues but does not compound. When it comes to investing, compound interest is better since it allows funds to grow at a faster rate than they would in an account with a simple interest rate. Compound interest comes into play when you’re calculating the annual percentage yield. That’s the annual rate of return or the annual cost of borrowing money. If borrowers can pay off their interest in a shorter period of time, they can then begin paying off their principal loan balance. They’ll be able to pay off their debt more quickly if they’re paying more interest up front. At the same, if a borrower has a loan that compounds often at a high interest rate, they’ll have higher monthly payments that might not be affordable. In that situation, a borrower might need to consider refinancing the loan to try to get a lower interest rate. For instance, if you’re in the process of paying off your private student loans, you can reach out to a lender to see if you can qualify for a reduced rate. Bottom LineUnderstanding the difference between simple and compound interest is crucial when you’re trying to pick the the right loan or find the best place to store your savings. If you’re a borrower who doesn’t want to get stuck with expensive debt that takes years to eliminate, you’ll probably want a loan with interest that doesn’t compound. But if you’re an investor looking to earn lots of money that you can use in retirement, it’s best to search for an account with interest that compounds frequently. Financial Planning Tips
Photo credit: ©iStock.com/solidcolours, ©iStock.com/TwilightEye, ©iStock.com/MachineHeadz Page 2Do you know enough about financial management to take care of all of your investing on your own? Or do you need help from a seasoned expert? That question comes up for millions of Americans each year. If any of these describe you, you could benefit from professional financial advice: 1. You’re retiring soon – Maximizing retirement income requires smart decisions around complex topics such as Social Security, 401(k) and IRA withdrawals. 2. You manage your own investments – Individual investors should check their strategies with unbiased third parties. You may be overlooking opportunities in your portfolio. 3. You have children – Whether you’re saving for college or planning their inheritance, there are several ways to ensure your children are taken care of. 4. You inherited money – Have you noticed lottery winners often declare bankruptcy? It can be difficult to manage sudden increases in wealth. 5. You have a financial advisor – Depending on how you chose your advisor, there may be a better one for you. Family referrals are convenient but don’t always produce results. 6. You’re divorcing – Untangling finances in a divorce can be messy. Impartial advice is key. 7. You want to build wealth – If you’re still decades from retirement, good decisions today can add thousands to your retirement accounts. See Your 3 Financial Advisor MatchesFinding a qualified financial advisor doesn’t have to be hard. SmartAsset’s free tool matches you with financial advisors in your area in 5 minutes. Each advisor has been pre-screened and vetted by SmartAsset and is held to a fiduciary standard. If you’re ready to be matched with local advisors that can help you achieve your financial goals, get started now.
Interest is the cost of borrowing money, where the borrower pays a fee to the lender for the loan. The interest, typically expressed as a percentage, can be either simple or compounded. Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period. Simple interest is calculated only on the principal amount of a loan or deposit, so it is easier to determine than compound interest.
Simple interest is calculated using the following formula: Simple Interest = P × r × n where: P = Principal amount r = Annual interest rate n = Term of loan, in years \begin{aligned} &\text{Simple Interest} = P \times r \times n \\ &\textbf{where:} \\ &P = \text{Principal amount} \\ &r = \text{Annual interest rate} \\ &n = \text{Term of loan, in years} \\ \end{aligned} Simple Interest=P×r×nwhere:P=Principal amountr=Annual interest raten=Term of loan, in years Generally, simple interest paid or received over a certain period is a fixed percentage of the principal amount that was borrowed or lent. For example, say a student obtains a simple-interest loan to pay one year of college tuition, which costs $18,000, and the annual interest rate on the loan is 6%. The student repays the loan over three years. The amount of simple interest paid is: $ 3 , 240 = $ 18 , 000 × 0.06 × 3 \begin{aligned} &\$3,240 = \$18,000 \times 0.06 \times 3 \\ \end{aligned} $3,240=$18,000×0.06×3 and the total amount paid is: $ 21 , 240 = $ 18 , 000 + $ 3 , 240 \begin{aligned} &\$21,240 = \$18,000 + \$3,240 \\ \end{aligned} $21,240=$18,000+$3,240 Compound interest accrues and is added to the accumulated interest of previous periods; it includes interest on interest, in other words. The formula for compound interest is: Compound Interest = P × ( 1 + r ) t − P where: P = Principal amount r = Annual interest rate t = Number of years interest is applied \begin{aligned} &\text{Compound Interest} = P \times \left ( 1 + r \right )^t - P \\ &\textbf{where:} \\ &P = \text{Principal amount} \\ &r = \text{Annual interest rate} \\ &t = \text{Number of years interest is applied} \\ \end{aligned} Compound Interest=P×(1+r)t−Pwhere:P=Principal amountr=Annual interest ratet=Number of years interest is applied It is calculated by multiplying the principal amount by one plus the annual interest rate raised to the number of compound periods, and then minus the reduction in the principal for that year. With compound interest, borrowers must pay interest on the interest as well as the principal. Below are some examples of simple and compound interest. Suppose you plunk $5,000 into a one-year certificate of deposit (CD) that pays simple interest at 3% per annum. The interest you earn after one year would be $150: $ 5 , 0 0 0 × 3 % × 1 \begin{aligned} &\$5,000 \times 3\% \times 1 \\ \end{aligned} $5,000×3%×1 Continuing with the above example, suppose your certificate of deposit is cashable at any time, with interest payable to you on a prorated basis. If you cash the CD after four months, how much would you earn in interest? You would receive $50: $ 5 , 0 0 0 × 3 % × 4 1 2 \begin{aligned} &\$5,000 \times 3\% \times \frac{ 4 }{ 12 } \\ \end{aligned} $5,000×3%×124 Suppose Bob borrows $500,000 for three years from his rich uncle, who agrees to charge Bob simple interest at 5% annually. How much would Bob have to pay in interest charges every year, and what would his total interest charges be after three years? (Assume the principal amount remains the same throughout the three years, i.e., the full loan amount is repaid after three years.) Bob would have to pay $25,000 in interest charges every year: $ 5 0 0 , 0 0 0 × 5 % × 1 \begin{aligned} &\$500,000 \times 5\% \times 1 \\ \end{aligned} $500,000×5%×1 or $75,000 in total interest charges after three years: $ 2 5 , 0 0 0 × 3 \begin{aligned} &\$25,000 \times 3 \\ \end{aligned} $25,000×3 Continuing with the above example, Bob needs to borrow an additional $500,000 for three years. Unfortunately, his rich uncle is tapped out. So, he takes a loan from the bank at an interest rate of 5% per year compounded annually, with the full loan amount and interest payable after three years. What would be the total interest paid by Bob? Since compound interest is calculated on the principal and accumulated interest, here's how it adds up: After Year One, Interest Payable = $ 2 5 , 0 0 0 , or $ 5 0 0 , 0 0 0 (Loan Principal) × 5 % × 1 After Year Two, Interest Payable = $ 2 6 , 2 5 0 , or $ 5 2 5 , 0 0 0 (Loan Principal + Year One Interest) × 5 % × 1 After Year Three, Interest Payable = $ 2 7 , 5 6 2 . 5 0 , or $ 5 5 1 , 2 5 0 Loan Principal + Interest for Years One and Two) × 5 % × 1 Total Interest Payable After Three Years = $ 7 8 , 8 1 2 . 5 0 , or $ 2 5 , 0 0 0 + $ 2 6 , 2 5 0 + $ 2 7 , 5 6 2 . 5 0 \begin{aligned} &\text{After Year One, Interest Payable} = \$25,000 \text{,} \\ &\text{or } \$500,000 \text{ (Loan Principal)} \times 5\% \times 1 \\ &\text{After Year Two, Interest Payable} = \$26,250 \text{,} \\ &\text{or } \$525,000 \text{ (Loan Principal + Year One Interest)} \\ &\times 5\% \times 1 \\ &\text{After Year Three, Interest Payable} = \$27,562.50 \text{,} \\ &\text{or } \$551,250 \text{ Loan Principal + Interest for Years One} \\ &\text{and Two)} \times 5\% \times 1 \\ &\text{Total Interest Payable After Three Years} = \$78,812.50 \text{,} \\ &\text{or } \$25,000 + \$26,250 + \$27,562.50 \\ \end{aligned} After Year One, Interest Payable=$25,000,or $500,000 (Loan Principal)×5%×1After Year Two, Interest Payable=$26,250,or $525,000 (Loan Principal + Year One Interest)×5%×1After Year Three, Interest Payable=$27,562.50,or $551,250 Loan Principal + Interest for Years Oneand Two)×5%×1Total Interest Payable After Three Years=$78,812.50,or $25,000+$26,250+$27,562.50 It can also be determined using the compound interest formula from above: Total Interest Payable After Three Years = $ 7 8 , 8 1 2 . 5 0 , or $ 5 0 0 , 0 0 0 (Loan Principal) × ( 1 + 0 . 0 5 ) 3 − $ 5 0 0 , 0 0 0 \begin{aligned} &\text{Total Interest Payable After Three Years} = \$78,812.50 \text{,} \\ &\text{or } \$500,000 \text{ (Loan Principal)} \times (1 + 0.05)^3 - \$500,000 \\ \end{aligned} Total Interest Payable After Three Years=$78,812.50,or $500,000 (Loan Principal)×(1+0.05)3−$500,000 This example shows how the formula for compound interest arises from paying interest on interest as well as principal. |
What is the difference between the compound interest and simple interest for the sum of $2000 over a period of 2 years?
Related Posts
Copyright © 2024 ShotOnMac Inc.
