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) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?

(2) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.

(4) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?

(6) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?

(7) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.

(8) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 8 years.

(10) What amount does David have to pay after 5 years if he takes a loan of $3400 at 5% simple interest?