Simple Interest
Math MCQs

Question :    How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?

Correct Answer  $6800

Solution & Explanation

Solution

Given,

Amount (A) = $7480

Rate of Simple Interest (R) = 2%

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

$7480 = P (1 + 2% × 5)

⇒ $7480 = P (1 + ²/₁₀₀ × 5)

⇒ $7480 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7480 = P (1 + ¹⁰/₁₀₀)

⇒ $7480 = P (^{100 + 10}/₁₀₀)

⇒ $7480 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7480

⇒ P = ⁷⁴⁸⁰/_¹¹⁰/100

⇒ P = 7480 × ¹⁰⁰/₁₁₀

⇒ P = ^{7480 × 100}/₁₁₀

⇒ P = ⁷⁴⁸⁰⁰⁰/₁₁₀

⇒ P = $6800

Thus, the sum borrowed (P) = $6800 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 7480, then the Principal = ¹⁰⁰/₁₁₀ × 7480

= ^{100 × 7480}/₁₁₀

= ⁷⁴⁸⁰⁰⁰/₁₁₀

= 6800

Thus, Principal = $6800

Thus, the sum borrowed = $6800 Answer

Similar Questions

(1) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(3) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 7 years.

(5) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(6) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.

(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?

(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

(9) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?

(10) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.