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 Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?

(2) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?

(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.

(6) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 5% simple interest?

(7) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?

(8) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.

(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 4 years.

(10) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.