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) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.

(2) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?

(3) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.

(6) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.

(8) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.

(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.

(10) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 8% simple interest?