Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

Correct Answer  $8701

Solution & Explanation

Solution

Given,

Principal (P) = $5650

Rate of Simple Interest (SI) = 6%

Time (t) = 9 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) = $5650 × 6% × 9

= $5650 ×⁶/₁₀₀ × 9

= ^{5650 × 6 × 9}/₁₀₀

= ^{33900 × 9}/₁₀₀

= ³⁰⁵¹⁰⁰/₁₀₀

= $3051

Thus, Simple Interest = $3051

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 = $5650 + $3051

= $8701

Thus, Amount to be paid = $8701 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 = $5650

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

And, Time (t) = 9 years

Thus, Amount (A)

= $5650 + ($5650 × 6% × 9)

= $5650 + ($5650 ×⁶/₁₀₀ × 9)

= $5650 + (^{5650 × 6 × 9}/₁₀₀)

= $5650 + (^{33900 × 9}/₁₀₀)

= $5650 + (³⁰⁵¹⁰⁰/₁₀₀)

= $5650 + $3051 = $8701

Thus, Amount (A) to be paid = $8701 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 $5650, the simple interest in 1 year

= ⁶/₁₀₀ × 5650

= ^{6 × 5650}/₁₀₀

= ³³⁹⁰⁰/₁₀₀ = $339

Thus, simple interest for 1 year = $339

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $339 × 9 = $3051

Thus, Simple Interest (SI) = $3051

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5650 + $3051

= $8701

Thus, Amount to be paid = $8701 Answer

Similar Questions

(1) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.

(2) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.

(4) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 7 years.

(7) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?

(8) If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 3 years.

(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.