Simple Interest
Math MCQs

Question :    Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.

Correct Answer  $8190

Solution & Explanation

Solution

Given,

Principal (P) = $5250

Rate of Simple Interest (SI) = 7%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $5250 × 7% × 8

= $5250 ×⁷/₁₀₀ × 8

= ^{5250 × 7 × 8}/₁₀₀

= ^{36750 × 8}/₁₀₀

= ²⁹⁴⁰⁰⁰/₁₀₀

= $2940

Thus, Simple Interest = $2940

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 = $5250 + $2940

= $8190

Thus, Amount to be paid = $8190 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 = $5250

Rate of Simple Interest (SI) or (R) = 7%

And, Time (t) = 8 years

Thus, Amount (A)

= $5250 + ($5250 × 7% × 8)

= $5250 + ($5250 ×⁷/₁₀₀ × 8)

= $5250 + (^{5250 × 7 × 8}/₁₀₀)

= $5250 + (^{36750 × 8}/₁₀₀)

= $5250 + (²⁹⁴⁰⁰⁰/₁₀₀)

= $5250 + $2940 = $8190

Thus, Amount (A) to be paid = $8190 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 7%

This, means, $7 per $100 per year

∵ For $100, the simple interest for 1 year = $7

∴ For $1, the simple interest for 1 year = ⁷/₁₀₀

∴ For $5250, the simple interest in 1 year

= ⁷/₁₀₀ × 5250

= ^{7 × 5250}/₁₀₀

= ³⁶⁷⁵⁰/₁₀₀ = $367.5

Thus, simple interest for 1 year = $367.5

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $367.5 × 8 = $2940

Thus, Simple Interest (SI) = $2940

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5250 + $2940

= $8190

Thus, Amount to be paid = $8190 Answer

Similar Questions

(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.

(2) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.

(3) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.

(4) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 3 years.

(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.

(7) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.

(8) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.

(9) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.

(10) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?