Simple Interest
Math MCQs

Question :    If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3400

Solution & Explanation

Solution

Given,

Amount (A) = $3672

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

$3672 = P (1 + 2% × 4)

⇒ $3672 = P (1 + ²/₁₀₀ × 4)

⇒ $3672 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3672 = P (1 + ⁸/₁₀₀)

⇒ $3672 = P (^{100 + 8}/₁₀₀)

⇒ $3672 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3672

⇒ P = ³⁶⁷²/_¹⁰⁸/100

⇒ P = 3672 × ¹⁰⁰/₁₀₈

⇒ P = ^{3672 × 100}/₁₀₈

⇒ P = ³⁶⁷²⁰⁰/₁₀₈

⇒ P = $3400

Thus, the sum borrowed (P) = $3400 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 3672, then the Principal = ¹⁰⁰/₁₀₈ × 3672

= ^{100 × 3672}/₁₀₈

= ³⁶⁷²⁰⁰/₁₀₈

= 3400

Thus, Principal = $3400

Thus, the sum borrowed = $3400 Answer

Similar Questions

(1) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.

(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?

(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

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

(5) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.

(6) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 10% simple interest?

(8) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 5% simple interest?

(9) Ashley had to pay $4959.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.