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) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.

(3) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.

(4) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?

(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 10% simple interest?

(7) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.

(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?

(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.

(10) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.