Simple Interest
Math MCQs

Question :    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) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.

(3) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?

(4) Betty had to pay $4632.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.

(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?

(7) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.

(8) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?

(9) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.

(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?