Simple Interest
Math MCQs

Question :    How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?

Correct Answer  $5100

Solution & Explanation

Solution

Given,

Amount (A) = $5610

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

$5610 = P (1 + 2% × 5)

⇒ $5610 = P (1 + ²/₁₀₀ × 5)

⇒ $5610 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5610 = P (1 + ¹⁰/₁₀₀)

⇒ $5610 = P (^{100 + 10}/₁₀₀)

⇒ $5610 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5610

⇒ P = ⁵⁶¹⁰/_¹¹⁰/100

⇒ P = 5610 × ¹⁰⁰/₁₁₀

⇒ P = ^{5610 × 100}/₁₁₀

⇒ P = ⁵⁶¹⁰⁰⁰/₁₁₀

⇒ P = $5100

Thus, the sum borrowed (P) = $5100 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 5610, then the Principal = ¹⁰⁰/₁₁₀ × 5610

= ^{100 × 5610}/₁₁₀

= ⁵⁶¹⁰⁰⁰/₁₁₀

= 5100

Thus, Principal = $5100

Thus, the sum borrowed = $5100 Answer

Similar Questions

(1) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.

(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.

(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 8 years.

(4) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?

(5) If Patricia paid $3654 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 4% simple interest?

(7) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.

(8) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

(9) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?

(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?