Simple Interest
Math MCQs

Question :  ( 1 of 10 )  How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?

Correct Answer  $5250

Solution & Explanation

Solution

Given,

Amount (A) = $5775

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

$5775 = P (1 + 2% × 5)

⇒ $5775 = P (1 + ²/₁₀₀ × 5)

⇒ $5775 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5775 = P (1 + ¹⁰/₁₀₀)

⇒ $5775 = P (^{100 + 10}/₁₀₀)

⇒ $5775 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5775

⇒ P = ⁵⁷⁷⁵/_¹¹⁰/100

⇒ P = 5775 × ¹⁰⁰/₁₁₀

⇒ P = ^{5775 × 100}/₁₁₀

⇒ P = ⁵⁷⁷⁵⁰⁰/₁₁₀

⇒ P = $5250

Thus, the sum borrowed (P) = $5250 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 5775, then the Principal = ¹⁰⁰/₁₁₀ × 5775

= ^{100 × 5775}/₁₁₀

= ⁵⁷⁷⁵⁰⁰/₁₁₀

= 5250

Thus, Principal = $5250

Thus, the sum borrowed = $5250 Answer

Similar Questions

(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.

(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.

(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.

(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?

(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(6) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.

(7) How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?

(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.

(9) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(10) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.