Simple Interest
Math MCQs

Question :    Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.

Correct Answer  $9000

Solution & Explanation

Solution

Given,

Principal (P) = $5000

Rate of Simple Interest (SI) = 10%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5000 × 10% × 8

= $5000 ×¹⁰/₁₀₀ × 8

= ^{5000 × 10 × 8}/₁₀₀

= ^{50000 × 8}/₁₀₀

= ⁴⁰⁰⁰⁰⁰/₁₀₀

= $4000

Thus, Simple Interest = $4000

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 = $5000 + $4000

= $9000

Thus, Amount to be paid = $9000 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 = $5000

Rate of Simple Interest (SI) or (R) = 10%

And, Time (t) = 8 years

Thus, Amount (A)

= $5000 + ($5000 × 10% × 8)

= $5000 + ($5000 ×¹⁰/₁₀₀ × 8)

= $5000 + (^{5000 × 10 × 8}/₁₀₀)

= $5000 + (^{50000 × 8}/₁₀₀)

= $5000 + (⁴⁰⁰⁰⁰⁰/₁₀₀)

= $5000 + $4000 = $9000

Thus, Amount (A) to be paid = $9000 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 10%

This, means, $10 per $100 per year

∵ For $100, the simple interest for 1 year = $10

∴ For $1, the simple interest for 1 year = ¹⁰/₁₀₀

∴ For $5000, the simple interest in 1 year

= ¹⁰/₁₀₀ × 5000

= ^{10 × 5000}/₁₀₀

= ⁵⁰⁰⁰⁰/₁₀₀ = $500

Thus, simple interest for 1 year = $500

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $500 × 8 = $4000

Thus, Simple Interest (SI) = $4000

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5000 + $4000

= $9000

Thus, Amount to be paid = $9000 Answer

Similar Questions

(1) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.

(2) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $7752 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.

(6) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.

(7) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?

(9) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?

(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.