Simple Interest
Math MCQs

Question :    If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4700

Solution & Explanation

Solution

Given,

Amount (A) = $5452

Rate of Simple Interest (R) = 4%

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

$5452 = P (1 + 4% × 4)

⇒ $5452 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5452 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5452 = P (1 + ¹⁶/₁₀₀)

⇒ $5452 = P (^{100 + 16}/₁₀₀)

⇒ $5452 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5452

⇒ P = ⁵⁴⁵²/_¹¹⁶/100

⇒ P = 5452 × ¹⁰⁰/₁₁₆

⇒ P = ^{5452 × 100}/₁₁₆

⇒ P = ⁵⁴⁵²⁰⁰/₁₁₆

⇒ 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 5452, then the Principal = ¹⁰⁰/₁₁₆ × 5452

= ^{100 × 5452}/₁₁₆

= ⁵⁴⁵²⁰⁰/₁₁₆

= 4700

Thus, Principal = $4700

Thus, the sum borrowed = $4700 Answer

Similar Questions

(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?

(2) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.

(3) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.

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

(5) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?

(6) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(7) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.

(9) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.