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 Paul borrowed a sum of $3850 at a 8% simple interest?

(2) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 7 years.

(3) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.

(6) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 9% simple interest?

(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.

(8) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 3 years.

(10) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.