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) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.

(3) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.

(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.

(6) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.

(7) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?

(8) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 2% simple interest?

(10) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.