Simple Interest
Math MCQs

Question :    Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.

Correct Answer  $9718

Solution & Explanation

Solution

Given,

Principal (P) = $5650

Rate of Simple Interest (SI) = 9%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $5650 × 9% × 8

= $5650 ×⁹/₁₀₀ × 8

= ^{5650 × 9 × 8}/₁₀₀

= ^{50850 × 8}/₁₀₀

= ⁴⁰⁶⁸⁰⁰/₁₀₀

= $4068

Thus, Simple Interest = $4068

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 = $5650 + $4068

= $9718

Thus, Amount to be paid = $9718 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 = $5650

Rate of Simple Interest (SI) or (R) = 9%

And, Time (t) = 8 years

Thus, Amount (A)

= $5650 + ($5650 × 9% × 8)

= $5650 + ($5650 ×⁹/₁₀₀ × 8)

= $5650 + (^{5650 × 9 × 8}/₁₀₀)

= $5650 + (^{50850 × 8}/₁₀₀)

= $5650 + (⁴⁰⁶⁸⁰⁰/₁₀₀)

= $5650 + $4068 = $9718

Thus, Amount (A) to be paid = $9718 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 9%

This, means, $9 per $100 per year

∵ For $100, the simple interest for 1 year = $9

∴ For $1, the simple interest for 1 year = ⁹/₁₀₀

∴ For $5650, the simple interest in 1 year

= ⁹/₁₀₀ × 5650

= ^{9 × 5650}/₁₀₀

= ⁵⁰⁸⁵⁰/₁₀₀ = $508.5

Thus, simple interest for 1 year = $508.5

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $508.5 × 8 = $4068

Thus, Simple Interest (SI) = $4068

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5650 + $4068

= $9718

Thus, Amount to be paid = $9718 Answer

Similar Questions

(1) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(2) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.

(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?

(5) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.

(7) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?

(8) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.

(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 2% simple interest?