Simple Interest
Math MCQs

Question :    If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4600

Solution & Explanation

Solution

Given,

Amount (A) = $4968

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

$4968 = P (1 + 2% × 4)

⇒ $4968 = P (1 + ²/₁₀₀ × 4)

⇒ $4968 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4968 = P (1 + ⁸/₁₀₀)

⇒ $4968 = P (^{100 + 8}/₁₀₀)

⇒ $4968 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4968

⇒ P = ⁴⁹⁶⁸/_¹⁰⁸/100

⇒ P = 4968 × ¹⁰⁰/₁₀₈

⇒ P = ^{4968 × 100}/₁₀₈

⇒ P = ⁴⁹⁶⁸⁰⁰/₁₀₈

⇒ P = $4600

Thus, the sum borrowed (P) = $4600 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 4968, then the Principal = ¹⁰⁰/₁₀₈ × 4968

= ^{100 × 4968}/₁₀₈

= ⁴⁹⁶⁸⁰⁰/₁₀₈

= 4600

Thus, Principal = $4600

Thus, the sum borrowed = $4600 Answer

Similar Questions

(1) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?

(2) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.

(3) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8528 to clear the loan, then find the time period of the loan.

(4) Margaret had to pay $4741.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(6) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 3 years.

(7) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 9% simple interest?

(8) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.

(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.

(10) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 2% simple interest?