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 after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.

(2) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?

(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?

(4) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

(5) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.

(7) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?

(8) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.

(9) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.

(10) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?