Simple Interest
Math MCQs

Question :    Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.

Correct Answer  $7000

Solution & Explanation

Solution

Given,

Principal (P) = $5000

Rate of Simple Interest (SI) = 5%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 8

= $5000 ×⁵/₁₀₀ × 8

= ^{5000 × 5 × 8}/₁₀₀

= ^{25000 × 8}/₁₀₀

= ²⁰⁰⁰⁰⁰/₁₀₀

= $2000

Thus, Simple Interest = $2000

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 + $2000

= $7000

Thus, Amount to be paid = $7000 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) = 5%

And, Time (t) = 8 years

Thus, Amount (A)

= $5000 + ($5000 × 5% × 8)

= $5000 + ($5000 ×⁵/₁₀₀ × 8)

= $5000 + (^{5000 × 5 × 8}/₁₀₀)

= $5000 + (^{25000 × 8}/₁₀₀)

= $5000 + (²⁰⁰⁰⁰⁰/₁₀₀)

= $5000 + $2000 = $7000

Thus, Amount (A) to be paid = $7000 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 5%

This, means, $5 per $100 per year

∵ For $100, the simple interest for 1 year = $5

∴ For $1, the simple interest for 1 year = ⁵/₁₀₀

∴ For $5000, the simple interest in 1 year

= ⁵/₁₀₀ × 5000

= ^{5 × 5000}/₁₀₀

= ²⁵⁰⁰⁰/₁₀₀ = $250

Thus, simple interest for 1 year = $250

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $250 × 8 = $2000

Thus, Simple Interest (SI) = $2000

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5000 + $2000

= $7000

Thus, Amount to be paid = $7000 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.

(2) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.

(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(4) How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?

(5) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?

(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?

(7) If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

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

(9) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.

(10) If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.