Simple Interest
Math MCQs

Question :    How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?

Correct Answer  $7150

Solution & Explanation

Solution

Given,

Amount (A) = $8937.5

Rate of Simple Interest (R) = 5%

Time (T) = 5 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

$8937.5 = P (1 + 5% × 5)

⇒ $8937.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8937.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8937.5 = P (1 + ²⁵/₁₀₀)

⇒ $8937.5 = P (^{100 + 25}/₁₀₀)

⇒ $8937.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8937.5

⇒ P = ^8937.5/_¹²⁵/100

⇒ P = 8937.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{8937.5 × 100}/₁₂₅

⇒ P = ⁸⁹³⁷⁵⁰/₁₂₅

⇒ P = $7150

Thus, the sum borrowed (P) = $7150 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 8937.5, then the Principal = ¹⁰⁰/₁₂₅ × 8937.5

= ^{100 × 8937.5}/₁₂₅

= ⁸⁹³⁷⁵⁰/₁₂₅

= 7150

Thus, Principal = $7150

Thus, the sum borrowed = $7150 Answer

Similar Questions

(1) If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.

(4) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?

(5) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?

(6) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.

(8) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.

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

(10) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.