Simple Interest
MCQs Math


Question:     How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?


Correct Answer  $7650

Solution And Explanation

Solution

Given,

Amount (A) = $9562.5

Rate of Simple Interest (R) = 5%

Time (T) = 5 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$9562.5 = P (1 + 5% × 5)

⇒ $9562.5 = P (1 + 5/100 × 5)

⇒ $9562.5 = P (1 + 5 × 5/100)

⇒ $9562.5 = P (1 + 25/100)

⇒ $9562.5 = P (100 + 25/100)

⇒ $9562.5 = P × 125/100

⇒ P × 125/100 = $9562.5

⇒ P = 9562.5/125/100

⇒ P = 9562.5 × 100/125

⇒ P = 9562.5 × 100/125

⇒ P = 956250/125

⇒ P = $7650

Thus, the sum borrowed (P) = $7650 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/125

∴ If the Amount is 9562.5, then the Principal = 100/125 × 9562.5

= 100 × 9562.5/125

= 956250/125

= 7650

Thus, Principal = $7650

Thus, the sum borrowed = $7650 Answer


Similar Questions

(1) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?

(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.

(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.

(4) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(5) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 6% simple interest?

(6) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.

(8) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 4 years.

(10) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.


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