Simple Interest
Math MCQs

Question :    If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3100

Solution & Explanation

Solution

Given,

Amount (A) = $3348

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

$3348 = P (1 + 2% × 4)

⇒ $3348 = P (1 + ²/₁₀₀ × 4)

⇒ $3348 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3348 = P (1 + ⁸/₁₀₀)

⇒ $3348 = P (^{100 + 8}/₁₀₀)

⇒ $3348 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3348

⇒ P = ³³⁴⁸/_¹⁰⁸/100

⇒ P = 3348 × ¹⁰⁰/₁₀₈

⇒ P = ^{3348 × 100}/₁₀₈

⇒ P = ³³⁴⁸⁰⁰/₁₀₈

⇒ P = $3100

Thus, the sum borrowed (P) = $3100 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 3348, then the Principal = ¹⁰⁰/₁₀₈ × 3348

= ^{100 × 3348}/₁₀₈

= ³³⁴⁸⁰⁰/₁₀₈

= 3100

Thus, Principal = $3100

Thus, the sum borrowed = $3100 Answer

Similar Questions

(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.

(2) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.

(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.

(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?

(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.

(7) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) If Lisa paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6724 to clear the loan, then find the time period of the loan.

(10) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.