Simple Interest
Math MCQs

Question :    Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.

Correct Answer  $7524

Solution & Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (SI) = 4%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5700 × 4% × 8

= $5700 ×⁴/₁₀₀ × 8

= ^{5700 × 4 × 8}/₁₀₀

= ^{22800 × 8}/₁₀₀

= ¹⁸²⁴⁰⁰/₁₀₀

= $1824

Thus, Simple Interest = $1824

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 = $5700 + $1824

= $7524

Thus, Amount to be paid = $7524 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 = $5700

Rate of Simple Interest (SI) or (R) = 4%

And, Time (t) = 8 years

Thus, Amount (A)

= $5700 + ($5700 × 4% × 8)

= $5700 + ($5700 ×⁴/₁₀₀ × 8)

= $5700 + (^{5700 × 4 × 8}/₁₀₀)

= $5700 + (^{22800 × 8}/₁₀₀)

= $5700 + (¹⁸²⁴⁰⁰/₁₀₀)

= $5700 + $1824 = $7524

Thus, Amount (A) to be paid = $7524 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 4%

This, means, $4 per $100 per year

∵ For $100, the simple interest for 1 year = $4

∴ For $1, the simple interest for 1 year = ⁴/₁₀₀

∴ For $5700, the simple interest in 1 year

= ⁴/₁₀₀ × 5700

= ^{4 × 5700}/₁₀₀

= ²²⁸⁰⁰/₁₀₀ = $228

Thus, simple interest for 1 year = $228

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $228 × 8 = $1824

Thus, Simple Interest (SI) = $1824

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5700 + $1824

= $7524

Thus, Amount to be paid = $7524 Answer

Similar Questions

(1) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 7% simple interest?

(2) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?

(3) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 7 years.

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

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.

(7) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.

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

(10) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.