Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.

Correct Answer  $6903

Solution & Explanation

Solution

Given,

Principal (P) = $5850

Rate of Simple Interest (SI) = 2%

Time (t) = 9 years

Thus, Amount (A) = ?

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

Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5850 × 2% × 9

= $5850 ײ/₁₀₀ × 9

= ^{5850 × 2 × 9}/₁₀₀

= ^{11700 × 9}/₁₀₀

= ¹⁰⁵³⁰⁰/₁₀₀

= $1053

Thus, Simple Interest = $1053

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 = $5850 + $1053

= $6903

Thus, Amount to be paid = $6903 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 = $5850

Rate of Simple Interest (SI) or (R) = 2%

And, Time (t) = 9 years

Thus, Amount (A)

= $5850 + ($5850 × 2% × 9)

= $5850 + ($5850 ײ/₁₀₀ × 9)

= $5850 + (^{5850 × 2 × 9}/₁₀₀)

= $5850 + (^{11700 × 9}/₁₀₀)

= $5850 + (¹⁰⁵³⁰⁰/₁₀₀)

= $5850 + $1053 = $6903

Thus, Amount (A) to be paid = $6903 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 2%

This, means, $2 per $100 per year

∵ For $100, the simple interest for 1 year = $2

∴ For $1, the simple interest for 1 year = ²/₁₀₀

∴ For $5850, the simple interest in 1 year

= ²/₁₀₀ × 5850

= ^{2 × 5850}/₁₀₀

= ¹¹⁷⁰⁰/₁₀₀ = $117

Thus, simple interest for 1 year = $117

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $117 × 9 = $1053

Thus, Simple Interest (SI) = $1053

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5850 + $1053

= $6903

Thus, Amount to be paid = $6903 Answer

Similar Questions

(1) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(2) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?

(4) If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?

(6) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?

(7) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?

(8) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.

(10) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?