Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.

Correct Answer  $9163

Solution & Explanation

Solution

Given,

Principal (P) = $5950

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) = $5950 × 6% × 9

= $5950 ×⁶/₁₀₀ × 9

= ^{5950 × 6 × 9}/₁₀₀

= ^{35700 × 9}/₁₀₀

= ³²¹³⁰⁰/₁₀₀

= $3213

Thus, Simple Interest = $3213

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 = $5950 + $3213

= $9163

Thus, Amount to be paid = $9163 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 = $5950

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

And, Time (t) = 9 years

Thus, Amount (A)

= $5950 + ($5950 × 6% × 9)

= $5950 + ($5950 ×⁶/₁₀₀ × 9)

= $5950 + (^{5950 × 6 × 9}/₁₀₀)

= $5950 + (^{35700 × 9}/₁₀₀)

= $5950 + (³²¹³⁰⁰/₁₀₀)

= $5950 + $3213 = $9163

Thus, Amount (A) to be paid = $9163 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 $5950, the simple interest in 1 year

= ⁶/₁₀₀ × 5950

= ^{6 × 5950}/₁₀₀

= ³⁵⁷⁰⁰/₁₀₀ = $357

Thus, simple interest for 1 year = $357

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $357 × 9 = $3213

Thus, Simple Interest (SI) = $3213

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5950 + $3213

= $9163

Thus, Amount to be paid = $9163 Answer

Similar Questions

(1) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(3) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?

(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?

(6) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.

(8) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?

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

(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 8 years.