Simple Interest
Math MCQs

Question :    Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.

Correct Answer  $8814

Solution & Explanation

Solution

Given,

Principal (P) = $5650

Rate of Simple Interest (SI) = 8%

Time (t) = 7 years

Thus, Amount (A) = ?

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

Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 7

= $5650 ×⁸/₁₀₀ × 7

= ^{5650 × 8 × 7}/₁₀₀

= ^{45200 × 7}/₁₀₀

= ³¹⁶⁴⁰⁰/₁₀₀

= $3164

Thus, Simple Interest = $3164

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 + $3164

= $8814

Thus, Amount to be paid = $8814 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) = 8%

And, Time (t) = 7 years

Thus, Amount (A)

= $5650 + ($5650 × 8% × 7)

= $5650 + ($5650 ×⁸/₁₀₀ × 7)

= $5650 + (^{5650 × 8 × 7}/₁₀₀)

= $5650 + (^{45200 × 7}/₁₀₀)

= $5650 + (³¹⁶⁴⁰⁰/₁₀₀)

= $5650 + $3164 = $8814

Thus, Amount (A) to be paid = $8814 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 8%

This, means, $8 per $100 per year

∵ For $100, the simple interest for 1 year = $8

∴ For $1, the simple interest for 1 year = ⁸/₁₀₀

∴ For $5650, the simple interest in 1 year

= ⁸/₁₀₀ × 5650

= ^{8 × 5650}/₁₀₀

= ⁴⁵²⁰⁰/₁₀₀ = $452

Thus, simple interest for 1 year = $452

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $452 × 7 = $3164

Thus, Simple Interest (SI) = $3164

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5650 + $3164

= $8814

Thus, Amount to be paid = $8814 Answer

Similar Questions

(1) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.

(3) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.

(5) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.

(6) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(7) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

(8) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.