What principal in investment will yield amounts of 6156 and 7290 in two and five years respectively at a specific equal rate of simple interest?

Computations for principal are applied for planning purposes. This is more of a futuristic point of view. If someone expects to earn a certain amount from investment or to pay for a loan or debt, thinking of what amount to invest or borrow will give the investor or borrower the idea to start in order to achieve the amount expected to earn or pay.

Remember that the interest is the product of the principal, rate of interest and time. Therefore, dividing the interest by the product of the interest rate and time will yield the principal.

where,

P means Principal

I means Interest

Also, the future amount is the sum of the principal and the interest. Therefore, the principal is just the difference between the future amount and the interest.

P = Future Amount - Interest

If only the future amount, time and interest rate are given, we can use the following formula to calculate the principall.

Note: The unit of time used is in years.

Question 7 Simple and Compound Interest Exercise 8.1

Next

Answer:

Here,

P = Rs 40000

A = Rs 4576.50

T = 2 years

Interest = Amount – Principal

= Rs 4576.50 – Rs 4050

= Rs 526.50

Let the rate of simple interest = R% per annum

Then,

R = (I × 100) / (P × T)

= (526.50 × 100) / (4050 × 2) % p.a.

On further calculation, we get,

= (526.50 × 10) / (405 × 2) % p.a.

= 5265 / 810 % p.a.

We get,

= 6.5% p.a.

Now,

P = Rs 1 lakh

= Rs 100000

R = 6.5% p.a.

T = 3 years

I = (P × R × T) / 100

= Rs (100000 × 6.5 × 3) / 100

We get,

= RS 1000 × 6.5 × 3

= Rs 19500

Amount = Principal + Interest

= Rs 100000 + Rs 19500

= Rs 119500

Video transcript

hello everybody welcome to lido learning channel my name is rachina chaudhary and we have to solve this question question is at a certain at a certain rate of simple interest rupees 4050 amounts to 576.50 in two years at the same rate of simple interest how much would rupees one lakh amounts to in three years so in second case we have to find the amount because this is given principle 1 lakh is principle so they are asking how much would be this amounts to but we need to calculate first of all rate for this we cannot find out without rate and without calculating simple interest now first of all we can see that there is no simple interest given in first case so let's find out simple interest so simple interest is always amount minus principle so this we are using for case first so simple interest would be 4576 minus 4050 after simplification we have 526.50 so this is simple interest now we will use the simple interest to calculate rate now we know that the formula of rate is simple interest multiplied by 100 upon principal multiplied by time so we just have calculated interest which is 526.50 multiplied by 100 and in denominator we will write principal multiply by time so principle is four zero five zero and time is two years so we can simplify it and after simplification we would get six point five percent as the rate so now we have calculated rate from the first case and simple interest also now we can see in the second case it is written at the same rate of simple interest how much amount how much 1 lakh would amount to so in second case principal is 1 lakh and time is 3 years rate is six percent we have to find amount so to find this amount first of all we need to find the simple interest so simple interest would be this is case second so simple interest is principal into rate into time upon hundred so after further calculation we would have simple interest as rupees nineteen thousand and five hundred now but we have to find amount we know that amount is equal to principal plus interest so principal in this case is 1 lakh and interest is nineteen thousand five hundred so the final answer is one lakh nineteen thousand five hundred so this is the final answer i hope you understand the method see you in my next video don't forget to like share and subscribe lead to learning channel thank you for watching

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Given:

A sum of money amounts to Rs. 2502 in three year and Rs. 3087 in five and a half year at the same rate of simple interest per annum.

Formula used:

simple interest = (principal × rate × time)/100

Calculation: 

Let the principal be 'P' and rate of interest = r%

In three year, amount = Rs. 2502

In five and a half year, amount = Rs. 3087

⇒ (5.5 - 3) year = Rs. (3087 - 2502)

so, 2.5 year = Rs. 585

⇒ 1 year = 585/(2.5) = Rs. 234

In three year = (585 × 3)/2.5 =Rs. 702

⇒ principal (P) = Rs. (2502 - 702) = Rs.1800

⇒ rate of interest (r) = (234/1800) × 100

⇒ r = 13%

∴ The required Rate of interest is 13%.

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By using the formula, find the amount and compound interest on: In how many yers will Rs 6250 amount to Rs 7290 at 8% per annum, compounded annually ?

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