Simple Interest
Math MCQs

Question :  ( 1 of 10 )  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) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 5% simple interest?

(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?

(3) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.

(4) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?

(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.

(7) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(8) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.

(9) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.

(10) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.