Simple Interest
Math MCQs

Question :    How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?

Correct Answer  $5200

Solution & Explanation

Solution

Given,

Amount (A) = $5720

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

$5720 = P (1 + 2% × 5)

⇒ $5720 = P (1 + ²/₁₀₀ × 5)

⇒ $5720 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5720 = P (1 + ¹⁰/₁₀₀)

⇒ $5720 = P (^{100 + 10}/₁₀₀)

⇒ $5720 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5720

⇒ P = ⁵⁷²⁰/_¹¹⁰/100

⇒ P = 5720 × ¹⁰⁰/₁₁₀

⇒ P = ^{5720 × 100}/₁₁₀

⇒ P = ⁵⁷²⁰⁰⁰/₁₁₀

⇒ P = $5200

Thus, the sum borrowed (P) = $5200 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 5720, then the Principal = ¹⁰⁰/₁₁₀ × 5720

= ^{100 × 5720}/₁₁₀

= ⁵⁷²⁰⁰⁰/₁₁₀

= 5200

Thus, Principal = $5200

Thus, the sum borrowed = $5200 Answer

Similar Questions

(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.

(2) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?

(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?

(4) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.

(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.

(7) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.

(8) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.

(9) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(10) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.