Simple Interest
Math MCQs

Question :    If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3900

Solution & Explanation

Solution

Given,

Amount (A) = $4212

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

$4212 = P (1 + 2% × 4)

⇒ $4212 = P (1 + ²/₁₀₀ × 4)

⇒ $4212 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4212 = P (1 + ⁸/₁₀₀)

⇒ $4212 = P (^{100 + 8}/₁₀₀)

⇒ $4212 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4212

⇒ P = ⁴²¹²/_¹⁰⁸/100

⇒ P = 4212 × ¹⁰⁰/₁₀₈

⇒ P = ^{4212 × 100}/₁₀₈

⇒ P = ⁴²¹²⁰⁰/₁₀₈

⇒ P = $3900

Thus, the sum borrowed (P) = $3900 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 4212, then the Principal = ¹⁰⁰/₁₀₈ × 4212

= ^{100 × 4212}/₁₀₈

= ⁴²¹²⁰⁰/₁₀₈

= 3900

Thus, Principal = $3900

Thus, the sum borrowed = $3900 Answer

Similar Questions

(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.

(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.

(3) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 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 $8778 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.

(6) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?

(7) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?

(8) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.

(9) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 6% simple interest?

(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?