Simple Interest
Math MCQs

Question :    Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.

Correct Answer  $9676

Solution & Explanation

Solution

Given,

Principal (P) = $5900

Rate of Simple Interest (SI) = 8%

Time (t) = 8 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) = $5900 × 8% × 8

= $5900 ×⁸/₁₀₀ × 8

= ^{5900 × 8 × 8}/₁₀₀

= ^{47200 × 8}/₁₀₀

= ³⁷⁷⁶⁰⁰/₁₀₀

= $3776

Thus, Simple Interest = $3776

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 = $5900 + $3776

= $9676

Thus, Amount to be paid = $9676 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 = $5900

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

And, Time (t) = 8 years

Thus, Amount (A)

= $5900 + ($5900 × 8% × 8)

= $5900 + ($5900 ×⁸/₁₀₀ × 8)

= $5900 + (^{5900 × 8 × 8}/₁₀₀)

= $5900 + (^{47200 × 8}/₁₀₀)

= $5900 + (³⁷⁷⁶⁰⁰/₁₀₀)

= $5900 + $3776 = $9676

Thus, Amount (A) to be paid = $9676 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 $5900, the simple interest in 1 year

= ⁸/₁₀₀ × 5900

= ^{8 × 5900}/₁₀₀

= ⁴⁷²⁰⁰/₁₀₀ = $472

Thus, simple interest for 1 year = $472

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $472 × 8 = $3776

Thus, Simple Interest (SI) = $3776

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5900 + $3776

= $9676

Thus, Amount to be paid = $9676 Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

(2) If Patricia paid $3654 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) What amount does John have to pay after 5 years if he takes a loan of $3200 at 8% simple interest?

(4) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.

(6) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.

(8) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

(9) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 7 years.