Simple Interest
Math MCQs

Question :    If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4900

Solution & Explanation

Solution

Given,

Amount (A) = $5292

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

$5292 = P (1 + 2% × 4)

⇒ $5292 = P (1 + ²/₁₀₀ × 4)

⇒ $5292 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $5292 = P (1 + ⁸/₁₀₀)

⇒ $5292 = P (^{100 + 8}/₁₀₀)

⇒ $5292 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $5292

⇒ P = ⁵²⁹²/_¹⁰⁸/100

⇒ P = 5292 × ¹⁰⁰/₁₀₈

⇒ P = ^{5292 × 100}/₁₀₈

⇒ P = ⁵²⁹²⁰⁰/₁₀₈

⇒ P = $4900

Thus, the sum borrowed (P) = $4900 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 5292, then the Principal = ¹⁰⁰/₁₀₈ × 5292

= ^{100 × 5292}/₁₀₈

= ⁵²⁹²⁰⁰/₁₀₈

= 4900

Thus, Principal = $4900

Thus, the sum borrowed = $4900 Answer

Similar Questions

(1) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.

(2) How much loan did Jason borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8855 to clear it?

(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?

(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.

(5) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.

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

(8) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 3 years.

(9) If Linda borrowed $3350 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

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