Simple Interest
Math MCQs

Question :    Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.

Correct Answer  $4158

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (SI) = 8%

Time (t) = 4 years

Thus, Amount (A) = ?

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

Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $3150 × 8% × 4

= $3150 ×⁸/₁₀₀ × 4

= ^{3150 × 8 × 4}/₁₀₀

= ^{25200 × 4}/₁₀₀

= ¹⁰⁰⁸⁰⁰/₁₀₀

= $1008

Thus, Simple Interest = $1008

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 = $3150 + $1008

= $4158

Thus, Amount to be paid = $4158 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 = $3150

Rate of Simple Interest (SI) or (R) = 8%

And, Time (t) = 4 years

Thus, Amount (A)

= $3150 + ($3150 × 8% × 4)

= $3150 + ($3150 ×⁸/₁₀₀ × 4)

= $3150 + (^{3150 × 8 × 4}/₁₀₀)

= $3150 + (^{25200 × 4}/₁₀₀)

= $3150 + (¹⁰⁰⁸⁰⁰/₁₀₀)

= $3150 + $1008 = $4158

Thus, Amount (A) to be paid = $4158 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 8%

This, means, $8 per $100 per year

∵ For $100, the simple interest for 1 year = $8

∴ For $1, the simple interest for 1 year = ⁸/₁₀₀

∴ For $3150, the simple interest in 1 year

= ⁸/₁₀₀ × 3150

= ^{8 × 3150}/₁₀₀

= ²⁵²⁰⁰/₁₀₀ = $252

Thus, simple interest for 1 year = $252

Therefore, simple interest for 4 years

= Simple interest for 1 year × 4

= $252 × 4 = $1008

Thus, Simple Interest (SI) = $1008

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3150 + $1008

= $4158

Thus, Amount to be paid = $4158 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?

(3) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?

(4) Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.

(6) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.

(8) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.

(10) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.