Simple Interest
Math MCQs

Question :    Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.

Correct Answer  $9632

Solution & Explanation

Solution

Given,

Principal (P) = $5600

Rate of Simple Interest (SI) = 9%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $5600 × 9% × 8

= $5600 ×⁹/₁₀₀ × 8

= ^{5600 × 9 × 8}/₁₀₀

= ^{50400 × 8}/₁₀₀

= ⁴⁰³²⁰⁰/₁₀₀

= $4032

Thus, Simple Interest = $4032

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 = $5600 + $4032

= $9632

Thus, Amount to be paid = $9632 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 = $5600

Rate of Simple Interest (SI) or (R) = 9%

And, Time (t) = 8 years

Thus, Amount (A)

= $5600 + ($5600 × 9% × 8)

= $5600 + ($5600 ×⁹/₁₀₀ × 8)

= $5600 + (^{5600 × 9 × 8}/₁₀₀)

= $5600 + (^{50400 × 8}/₁₀₀)

= $5600 + (⁴⁰³²⁰⁰/₁₀₀)

= $5600 + $4032 = $9632

Thus, Amount (A) to be paid = $9632 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 9%

This, means, $9 per $100 per year

∵ For $100, the simple interest for 1 year = $9

∴ For $1, the simple interest for 1 year = ⁹/₁₀₀

∴ For $5600, the simple interest in 1 year

= ⁹/₁₀₀ × 5600

= ^{9 × 5600}/₁₀₀

= ⁵⁰⁴⁰⁰/₁₀₀ = $504

Thus, simple interest for 1 year = $504

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $504 × 8 = $4032

Thus, Simple Interest (SI) = $4032

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5600 + $4032

= $9632

Thus, Amount to be paid = $9632 Answer

Similar Questions

(1) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?

(2) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(4) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.

(5) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.

(6) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?

(7) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.

(9) Ashley had to pay $4959.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 7% simple interest?