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) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.

(2) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 2% simple interest?

(4) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.

(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?

(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.

(7) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.

(8) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 4 years.

(10) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.