Simple Interest
Math MCQs

Question :    How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?

Correct Answer  $5050

Solution & Explanation

Solution

Given,

Amount (A) = $5555

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

$5555 = P (1 + 2% × 5)

⇒ $5555 = P (1 + ²/₁₀₀ × 5)

⇒ $5555 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5555 = P (1 + ¹⁰/₁₀₀)

⇒ $5555 = P (^{100 + 10}/₁₀₀)

⇒ $5555 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5555

⇒ P = ⁵⁵⁵⁵/_¹¹⁰/100

⇒ P = 5555 × ¹⁰⁰/₁₁₀

⇒ P = ^{5555 × 100}/₁₁₀

⇒ P = ⁵⁵⁵⁵⁰⁰/₁₁₀

⇒ P = $5050

Thus, the sum borrowed (P) = $5050 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 5555, then the Principal = ¹⁰⁰/₁₁₀ × 5555

= ^{100 × 5555}/₁₁₀

= ⁵⁵⁵⁵⁰⁰/₁₁₀

= 5050

Thus, Principal = $5050

Thus, the sum borrowed = $5050 Answer

Similar Questions

(1) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 4 years.

(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.

(3) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(4) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.

(5) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.

(6) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 4 years.

(8) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.

(10) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.