Simple Interest
Math MCQs

Question :    How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?

Correct Answer  $7750

Solution & Explanation

Solution

Given,

Amount (A) = $8525

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

$8525 = P (1 + 2% × 5)

⇒ $8525 = P (1 + ²/₁₀₀ × 5)

⇒ $8525 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8525 = P (1 + ¹⁰/₁₀₀)

⇒ $8525 = P (^{100 + 10}/₁₀₀)

⇒ $8525 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8525

⇒ P = ⁸⁵²⁵/_¹¹⁰/100

⇒ P = 8525 × ¹⁰⁰/₁₁₀

⇒ P = ^{8525 × 100}/₁₁₀

⇒ P = ⁸⁵²⁵⁰⁰/₁₁₀

⇒ P = $7750

Thus, the sum borrowed (P) = $7750 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 8525, then the Principal = ¹⁰⁰/₁₁₀ × 8525

= ^{100 × 8525}/₁₁₀

= ⁸⁵²⁵⁰⁰/₁₁₀

= 7750

Thus, Principal = $7750

Thus, the sum borrowed = $7750 Answer

Similar Questions

(1) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?

(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?

(3) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.

(5) What amount will be due after 2 years if David borrowed a sum of $3200 at a 4% simple interest?

(6) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.

(8) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.

(10) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.