Simple Interest
Math MCQs

Question :    Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.

Correct Answer  $8330

Solution & Explanation

Solution

Given,

Principal (P) = $5950

Rate of Simple Interest (SI) = 5%

Time (t) = 8 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) = $5950 × 5% × 8

= $5950 ×⁵/₁₀₀ × 8

= ^{5950 × 5 × 8}/₁₀₀

= ^{29750 × 8}/₁₀₀

= ²³⁸⁰⁰⁰/₁₀₀

= $2380

Thus, Simple Interest = $2380

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 = $5950 + $2380

= $8330

Thus, Amount to be paid = $8330 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 = $5950

Rate of Simple Interest (SI) or (R) = 5%

And, Time (t) = 8 years

Thus, Amount (A)

= $5950 + ($5950 × 5% × 8)

= $5950 + ($5950 ×⁵/₁₀₀ × 8)

= $5950 + (^{5950 × 5 × 8}/₁₀₀)

= $5950 + (^{29750 × 8}/₁₀₀)

= $5950 + (²³⁸⁰⁰⁰/₁₀₀)

= $5950 + $2380 = $8330

Thus, Amount (A) to be paid = $8330 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 $5950, the simple interest in 1 year

= ⁵/₁₀₀ × 5950

= ^{5 × 5950}/₁₀₀

= ²⁹⁷⁵⁰/₁₀₀ = $297.5

Thus, simple interest for 1 year = $297.5

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $297.5 × 8 = $2380

Thus, Simple Interest (SI) = $2380

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5950 + $2380

= $8330

Thus, Amount to be paid = $8330 Answer

Similar Questions

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

(2) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.

(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.

(5) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?

(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.

(7) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?

(8) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.

(10) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.