Simple Interest
Math MCQs

Question :    If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4550

Solution & Explanation

Solution

Given,

Amount (A) = $5460

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

$5460 = P (1 + 5% × 4)

⇒ $5460 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5460 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5460 = P (1 + ²⁰/₁₀₀)

⇒ $5460 = P (^{100 + 20}/₁₀₀)

⇒ $5460 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5460

⇒ P = ⁵⁴⁶⁰/_¹²⁰/100

⇒ P = 5460 × ¹⁰⁰/₁₂₀

⇒ P = ^{5460 × 100}/₁₂₀

⇒ P = ⁵⁴⁶⁰⁰⁰/₁₂₀

⇒ P = $4550

Thus, the sum borrowed (P) = $4550 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 5460, then the Principal = ¹⁰⁰/₁₂₀ × 5460

= ^{100 × 5460}/₁₂₀

= ⁵⁴⁶⁰⁰⁰/₁₂₀

= 4550

Thus, Principal = $4550

Thus, the sum borrowed = $4550 Answer

Similar Questions

(1) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.

(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?

(4) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?

(6) Richard had to pay $3924 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) William had to pay $3920 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.

(9) If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.