Simple Interest
Math MCQs

Question :    If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3850

Solution & Explanation

Solution

Given,

Amount (A) = $4158

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

$4158 = P (1 + 2% × 4)

⇒ $4158 = P (1 + ²/₁₀₀ × 4)

⇒ $4158 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4158 = P (1 + ⁸/₁₀₀)

⇒ $4158 = P (^{100 + 8}/₁₀₀)

⇒ $4158 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4158

⇒ P = ⁴¹⁵⁸/_¹⁰⁸/100

⇒ P = 4158 × ¹⁰⁰/₁₀₈

⇒ P = ^{4158 × 100}/₁₀₈

⇒ P = ⁴¹⁵⁸⁰⁰/₁₀₈

⇒ P = $3850

Thus, the sum borrowed (P) = $3850 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 4158, then the Principal = ¹⁰⁰/₁₀₈ × 4158

= ^{100 × 4158}/₁₀₈

= ⁴¹⁵⁸⁰⁰/₁₀₈

= 3850

Thus, Principal = $3850

Thus, the sum borrowed = $3850 Answer

Similar Questions

(1) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?

(2) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.

(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?

(5) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 3 years.

(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.

(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.

(8) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.

(9) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.

(10) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.