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) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?

(2) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?

(4) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.

(5) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?

(6) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?

(7) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.

(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.

(9) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.

(10) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?