Simple Interest
Math MCQs

Question :    Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.

Correct Answer  $8140

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (SI) = 6%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5500 × 6% × 8

= $5500 ×⁶/₁₀₀ × 8

= ^{5500 × 6 × 8}/₁₀₀

= ^{33000 × 8}/₁₀₀

= ²⁶⁴⁰⁰⁰/₁₀₀

= $2640

Thus, Simple Interest = $2640

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 = $5500 + $2640

= $8140

Thus, Amount to be paid = $8140 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 = $5500

Rate of Simple Interest (SI) or (R) = 6%

And, Time (t) = 8 years

Thus, Amount (A)

= $5500 + ($5500 × 6% × 8)

= $5500 + ($5500 ×⁶/₁₀₀ × 8)

= $5500 + (^{5500 × 6 × 8}/₁₀₀)

= $5500 + (^{33000 × 8}/₁₀₀)

= $5500 + (²⁶⁴⁰⁰⁰/₁₀₀)

= $5500 + $2640 = $8140

Thus, Amount (A) to be paid = $8140 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 6%

This, means, $6 per $100 per year

∵ For $100, the simple interest for 1 year = $6

∴ For $1, the simple interest for 1 year = ⁶/₁₀₀

∴ For $5500, the simple interest in 1 year

= ⁶/₁₀₀ × 5500

= ^{6 × 5500}/₁₀₀

= ³³⁰⁰⁰/₁₀₀ = $330

Thus, simple interest for 1 year = $330

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $330 × 8 = $2640

Thus, Simple Interest (SI) = $2640

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5500 + $2640

= $8140

Thus, Amount to be paid = $8140 Answer

Similar Questions

(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?

(2) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(3) If Patricia paid $3402 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.

(6) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(7) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 4 years.

(10) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.