Simple Interest
Math MCQs

Question :    Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.

Correct Answer  $7006

Solution & Explanation

Solution

Given,

Principal (P) = $5650

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) = $5650 × 3% × 8

= $5650 ׳/₁₀₀ × 8

= ^{5650 × 3 × 8}/₁₀₀

= ^{16950 × 8}/₁₀₀

= ¹³⁵⁶⁰⁰/₁₀₀

= $1356

Thus, Simple Interest = $1356

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 + $1356

= $7006

Thus, Amount to be paid = $7006 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) = 3%

And, Time (t) = 8 years

Thus, Amount (A)

= $5650 + ($5650 × 3% × 8)

= $5650 + ($5650 ׳/₁₀₀ × 8)

= $5650 + (^{5650 × 3 × 8}/₁₀₀)

= $5650 + (^{16950 × 8}/₁₀₀)

= $5650 + (¹³⁵⁶⁰⁰/₁₀₀)

= $5650 + $1356 = $7006

Thus, Amount (A) to be paid = $7006 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 $5650, the simple interest in 1 year

= ³/₁₀₀ × 5650

= ^{3 × 5650}/₁₀₀

= ¹⁶⁹⁵⁰/₁₀₀ = $169.5

Thus, simple interest for 1 year = $169.5

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $169.5 × 8 = $1356

Thus, Simple Interest (SI) = $1356

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5650 + $1356

= $7006

Thus, Amount to be paid = $7006 Answer

Similar Questions

(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.

(2) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?

(3) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?

(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?

(6) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.

(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) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(9) If Richard borrowed $3600 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.