Simple Interest
Math MCQs

Question :    Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.

Correct Answer  $7627.5

Solution & Explanation

Solution

Given,

Principal (P) = $5650

Rate of Simple Interest (SI) = 5%

Time (t) = 7 years

Thus, Amount (A) = ?

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

Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 7

= $5650 ×⁵/₁₀₀ × 7

= ^{5650 × 5 × 7}/₁₀₀

= ^{28250 × 7}/₁₀₀

= ¹⁹⁷⁷⁵⁰/₁₀₀

= $1977.5

Thus, Simple Interest = $1977.5

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 + $1977.5

= $7627.5

Thus, Amount to be paid = $7627.5 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) = 5%

And, Time (t) = 7 years

Thus, Amount (A)

= $5650 + ($5650 × 5% × 7)

= $5650 + ($5650 ×⁵/₁₀₀ × 7)

= $5650 + (^{5650 × 5 × 7}/₁₀₀)

= $5650 + (^{28250 × 7}/₁₀₀)

= $5650 + (¹⁹⁷⁷⁵⁰/₁₀₀)

= $5650 + $1977.5 = $7627.5

Thus, Amount (A) to be paid = $7627.5 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 5%

This, means, $5 per $100 per year

∵ For $100, the simple interest for 1 year = $5

∴ For $1, the simple interest for 1 year = ⁵/₁₀₀

∴ For $5650, the simple interest in 1 year

= ⁵/₁₀₀ × 5650

= ^{5 × 5650}/₁₀₀

= ²⁸²⁵⁰/₁₀₀ = $282.5

Thus, simple interest for 1 year = $282.5

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $282.5 × 7 = $1977.5

Thus, Simple Interest (SI) = $1977.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5650 + $1977.5

= $7627.5

Thus, Amount to be paid = $7627.5 Answer

Similar Questions

(1) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 3 years.

(3) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.

(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.

(6) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?

(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?

(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 10% simple interest?

(9) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.

(10) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.