Simple Interest
Math MCQs

Question :    How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?

Correct Answer  $7800

Solution & Explanation

Solution

Given,

Amount (A) = $8580

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

$8580 = P (1 + 2% × 5)

⇒ $8580 = P (1 + ²/₁₀₀ × 5)

⇒ $8580 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8580 = P (1 + ¹⁰/₁₀₀)

⇒ $8580 = P (^{100 + 10}/₁₀₀)

⇒ $8580 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8580

⇒ P = ⁸⁵⁸⁰/_¹¹⁰/100

⇒ P = 8580 × ¹⁰⁰/₁₁₀

⇒ P = ^{8580 × 100}/₁₁₀

⇒ P = ⁸⁵⁸⁰⁰⁰/₁₁₀

⇒ P = $7800

Thus, the sum borrowed (P) = $7800 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 8580, then the Principal = ¹⁰⁰/₁₁₀ × 8580

= ^{100 × 8580}/₁₁₀

= ⁸⁵⁸⁰⁰⁰/₁₁₀

= 7800

Thus, Principal = $7800

Thus, the sum borrowed = $7800 Answer

Similar Questions

(1) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.

(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 6% simple interest?

(3) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.

(4) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.

(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.

(6) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.

(7) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?

(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?

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

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.