Simple Interest
Math MCQs

Question :    How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?

Correct Answer  $7350

Solution & Explanation

Solution

Given,

Amount (A) = $8085

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

$8085 = P (1 + 2% × 5)

⇒ $8085 = P (1 + ²/₁₀₀ × 5)

⇒ $8085 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8085 = P (1 + ¹⁰/₁₀₀)

⇒ $8085 = P (^{100 + 10}/₁₀₀)

⇒ $8085 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8085

⇒ P = ⁸⁰⁸⁵/_¹¹⁰/100

⇒ P = 8085 × ¹⁰⁰/₁₁₀

⇒ P = ^{8085 × 100}/₁₁₀

⇒ P = ⁸⁰⁸⁵⁰⁰/₁₁₀

⇒ P = $7350

Thus, the sum borrowed (P) = $7350 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 8085, then the Principal = ¹⁰⁰/₁₁₀ × 8085

= ^{100 × 8085}/₁₁₀

= ⁸⁰⁸⁵⁰⁰/₁₁₀

= 7350

Thus, Principal = $7350

Thus, the sum borrowed = $7350 Answer

Similar Questions

(1) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?

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

(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.

(4) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.

(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 8 years.

(6) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.

(7) 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.

(8) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.

(9) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $10498 to clear the loan, then find the time period of the loan.

(10) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 7% simple interest?