Simple Interest
Math MCQs

Question :    Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.

Correct Answer  $7254

Solution & Explanation

Solution

Given,

Principal (P) = $5850

Rate of Simple Interest (SI) = 3%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $5850 × 3% × 8

= $5850 ׳/₁₀₀ × 8

= ^{5850 × 3 × 8}/₁₀₀

= ^{17550 × 8}/₁₀₀

= ¹⁴⁰⁴⁰⁰/₁₀₀

= $1404

Thus, Simple Interest = $1404

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 = $5850 + $1404

= $7254

Thus, Amount to be paid = $7254 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 = $5850

Rate of Simple Interest (SI) or (R) = 3%

And, Time (t) = 8 years

Thus, Amount (A)

= $5850 + ($5850 × 3% × 8)

= $5850 + ($5850 ׳/₁₀₀ × 8)

= $5850 + (^{5850 × 3 × 8}/₁₀₀)

= $5850 + (^{17550 × 8}/₁₀₀)

= $5850 + (¹⁴⁰⁴⁰⁰/₁₀₀)

= $5850 + $1404 = $7254

Thus, Amount (A) to be paid = $7254 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 3%

This, means, $3 per $100 per year

∵ For $100, the simple interest for 1 year = $3

∴ For $1, the simple interest for 1 year = ³/₁₀₀

∴ For $5850, the simple interest in 1 year

= ³/₁₀₀ × 5850

= ^{3 × 5850}/₁₀₀

= ¹⁷⁵⁵⁰/₁₀₀ = $175.5

Thus, simple interest for 1 year = $175.5

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $175.5 × 8 = $1404

Thus, Simple Interest (SI) = $1404

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5850 + $1404

= $7254

Thus, Amount to be paid = $7254 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.

(2) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

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

(4) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(6) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?

(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

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

(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.