Simple Interest
Math MCQs

Question :    If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3500

Solution & Explanation

Solution

Given,

Amount (A) = $3780

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

$3780 = P (1 + 2% × 4)

⇒ $3780 = P (1 + ²/₁₀₀ × 4)

⇒ $3780 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3780 = P (1 + ⁸/₁₀₀)

⇒ $3780 = P (^{100 + 8}/₁₀₀)

⇒ $3780 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3780

⇒ P = ³⁷⁸⁰/_¹⁰⁸/100

⇒ P = 3780 × ¹⁰⁰/₁₀₈

⇒ P = ^{3780 × 100}/₁₀₈

⇒ P = ³⁷⁸⁰⁰⁰/₁₀₈

⇒ P = $3500

Thus, the sum borrowed (P) = $3500 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 3780, then the Principal = ¹⁰⁰/₁₀₈ × 3780

= ^{100 × 3780}/₁₀₈

= ³⁷⁸⁰⁰⁰/₁₀₈

= 3500

Thus, Principal = $3500

Thus, the sum borrowed = $3500 Answer

Similar Questions

(1) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 10% simple interest?

(2) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.

(3) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.

(4) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.

(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.

(7) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.

(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(10) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?