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) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.

(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.

(3) How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?

(4) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?

(5) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 3 years.

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.

(7) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 3% simple interest?

(8) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 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 $5920 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?