Simple Interest
Math MCQs

Question :    If Andrew paid $5760 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4800

Solution & Explanation

Solution

Given,

Amount (A) = $5760

Rate of Simple Interest (R) = 5%

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

$5760 = P (1 + 5% × 4)

⇒ $5760 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5760 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5760 = P (1 + ²⁰/₁₀₀)

⇒ $5760 = P (^{100 + 20}/₁₀₀)

⇒ $5760 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5760

⇒ P = ⁵⁷⁶⁰/_¹²⁰/100

⇒ P = 5760 × ¹⁰⁰/₁₂₀

⇒ P = ^{5760 × 100}/₁₂₀

⇒ P = ⁵⁷⁶⁰⁰⁰/₁₂₀

⇒ P = $4800

Thus, the sum borrowed (P) = $4800 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 5760, then the Principal = ¹⁰⁰/₁₂₀ × 5760

= ^{100 × 5760}/₁₂₀

= ⁵⁷⁶⁰⁰⁰/₁₂₀

= 4800

Thus, Principal = $4800

Thus, the sum borrowed = $4800 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 4 years.

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

(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 5% simple interest?

(5) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.

(6) How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?

(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) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?

(10) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.