Simple Interest
Math MCQs

Question :    How much loan did Emily borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8437.5 to clear it?

Correct Answer  $6750

Solution & Explanation

Solution

Given,

Amount (A) = $8437.5

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

$8437.5 = P (1 + 5% × 5)

⇒ $8437.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8437.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8437.5 = P (1 + ²⁵/₁₀₀)

⇒ $8437.5 = P (^{100 + 25}/₁₀₀)

⇒ $8437.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8437.5

⇒ P = ^8437.5/_¹²⁵/100

⇒ P = 8437.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{8437.5 × 100}/₁₂₅

⇒ P = ⁸⁴³⁷⁵⁰/₁₂₅

⇒ P = $6750

Thus, the sum borrowed (P) = $6750 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 8437.5, then the Principal = ¹⁰⁰/₁₂₅ × 8437.5

= ^{100 × 8437.5}/₁₂₅

= ⁸⁴³⁷⁵⁰/₁₂₅

= 6750

Thus, Principal = $6750

Thus, the sum borrowed = $6750 Answer

Similar Questions

(1) If Jessica paid $4050 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?

(3) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.

(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?

(6) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.

(7) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 4 years.

(10) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 4 years.