Simple Interest
Math MCQs

Question :    How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?

Correct Answer  $8000

Solution & Explanation

Solution

Given,

Amount (A) = $8800

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

$8800 = P (1 + 2% × 5)

⇒ $8800 = P (1 + ²/₁₀₀ × 5)

⇒ $8800 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8800 = P (1 + ¹⁰/₁₀₀)

⇒ $8800 = P (^{100 + 10}/₁₀₀)

⇒ $8800 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8800

⇒ P = ⁸⁸⁰⁰/_¹¹⁰/100

⇒ P = 8800 × ¹⁰⁰/₁₁₀

⇒ P = ^{8800 × 100}/₁₁₀

⇒ P = ⁸⁸⁰⁰⁰⁰/₁₁₀

⇒ P = $8000

Thus, the sum borrowed (P) = $8000 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 8800, then the Principal = ¹⁰⁰/₁₁₀ × 8800

= ^{100 × 8800}/₁₁₀

= ⁸⁸⁰⁰⁰⁰/₁₁₀

= 8000

Thus, Principal = $8000

Thus, the sum borrowed = $8000 Answer

Similar Questions

(1) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.

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

(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?

(5) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?

(6) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?

(7) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.

(8) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.

(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.