Simple Interest
Math MCQs

Question :    How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?

Correct Answer  $7450

Solution & Explanation

Solution

Given,

Amount (A) = $8195

Rate of Simple Interest (R) = 2%

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

$8195 = P (1 + 2% × 5)

⇒ $8195 = P (1 + ²/₁₀₀ × 5)

⇒ $8195 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8195 = P (1 + ¹⁰/₁₀₀)

⇒ $8195 = P (^{100 + 10}/₁₀₀)

⇒ $8195 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8195

⇒ P = ⁸¹⁹⁵/_¹¹⁰/100

⇒ P = 8195 × ¹⁰⁰/₁₁₀

⇒ P = ^{8195 × 100}/₁₁₀

⇒ P = ⁸¹⁹⁵⁰⁰/₁₁₀

⇒ P = $7450

Thus, the sum borrowed (P) = $7450 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 8195, then the Principal = ¹⁰⁰/₁₁₀ × 8195

= ^{100 × 8195}/₁₁₀

= ⁸¹⁹⁵⁰⁰/₁₁₀

= 7450

Thus, Principal = $7450

Thus, the sum borrowed = $7450 Answer

Similar Questions

(1) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.

(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?

(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?

(5) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.

(6) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?

(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.

(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.

(9) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.