Simple Interest
Math MCQs

Question :    If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4700

Solution & Explanation

Solution

Given,

Amount (A) = $5076

Rate of Simple Interest (R) = 2%

Time (T) = 4 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

$5076 = P (1 + 2% × 4)

⇒ $5076 = P (1 + ²/₁₀₀ × 4)

⇒ $5076 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $5076 = P (1 + ⁸/₁₀₀)

⇒ $5076 = P (^{100 + 8}/₁₀₀)

⇒ $5076 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $5076

⇒ P = ⁵⁰⁷⁶/_¹⁰⁸/100

⇒ P = 5076 × ¹⁰⁰/₁₀₈

⇒ P = ^{5076 × 100}/₁₀₈

⇒ P = ⁵⁰⁷⁶⁰⁰/₁₀₈

⇒ P = $4700

Thus, the sum borrowed (P) = $4700 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 = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 5076, then the Principal = ¹⁰⁰/₁₀₈ × 5076

= ^{100 × 5076}/₁₀₈

= ⁵⁰⁷⁶⁰⁰/₁₀₈

= 4700

Thus, Principal = $4700

Thus, the sum borrowed = $4700 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.

(2) What amount will be due after 2 years if John borrowed a sum of $3100 at a 10% simple interest?

(3) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?

(4) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.

(5) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?

(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 8 years.

(8) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.

(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.