Simple Interest
Math MCQs

Question :    Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.

Correct Answer  $7800

Solution & Explanation

Solution

Given,

Principal (P) = $5000

Rate of Simple Interest (SI) = 7%

Time (t) = 8 years

Thus, Amount (A) = ?

The Rate of Interest is always calculated per annum, i.e. per year.

Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% per annum.

Method (1) Using Formula

Calculation of Simple Interest

Formula to Calculate Simple Interest

Simple Interest (SI) = Principal × Rate × Time

Thus, Simple Interest (SI) = $5000 × 7% × 8

= $5000 ×⁷/₁₀₀ × 8

= ^{5000 × 7 × 8}/₁₀₀

= ^{35000 × 8}/₁₀₀

= ²⁸⁰⁰⁰⁰/₁₀₀

= $2800

Thus, Simple Interest = $2800

Calculation of Amount

The total money paid to the lender by a borrower is called the Amount.

In other words, sum of priciple and interest is called the Amount.

Formula to Calculate the Amount

Amount = Principal + Interest

Thus, Amount = $5000 + $2800

= $7800

Thus, Amount to be paid = $7800 Answer

Method (2)

Calculation of Amount when Principal, Rate of Simple Interest and Time are given

Calculation of Amount directly using Principal, SI, and Time

Formula to calculate the Amount

Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)

⇒ A = P + PRT

Here in the question, P = $5000

Rate of Simple Interest (SI) or (R) = 7%

And, Time (t) = 8 years

Thus, Amount (A)

= $5000 + ($5000 × 7% × 8)

= $5000 + ($5000 ×⁷/₁₀₀ × 8)

= $5000 + (^{5000 × 7 × 8}/₁₀₀)

= $5000 + (^{35000 × 8}/₁₀₀)

= $5000 + (²⁸⁰⁰⁰⁰/₁₀₀)

= $5000 + $2800 = $7800

Thus, Amount (A) to be paid = $7800 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 7%

This, means, $7 per $100 per year

∵ For $100, the simple interest for 1 year = $7

∴ For $1, the simple interest for 1 year = ⁷/₁₀₀

∴ For $5000, the simple interest in 1 year

= ⁷/₁₀₀ × 5000

= ^{7 × 5000}/₁₀₀

= ³⁵⁰⁰⁰/₁₀₀ = $350

Thus, simple interest for 1 year = $350

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $350 × 8 = $2800

Thus, Simple Interest (SI) = $2800

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5000 + $2800

= $7800

Thus, Amount to be paid = $7800 Answer

Similar Questions

(1) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.

(2) What amount does David have to pay after 6 years if he takes a loan of $3400 at 4% simple interest?

(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.

(4) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?

(5) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(6) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?

(8) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.

(9) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?