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) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.

(4) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.

(5) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.

(7) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?

(8) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.

(9) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?