Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.

Correct Answer  $7950

Solution & Explanation

Solution

Given,

Principal (P) = $5300

Rate of Simple Interest (SI) = 5%

Time (t) = 10 years

Thus, Amount (A) = ?

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

Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5300 × 5% × 10

= $5300 ×⁵/₁₀₀ × 10

= ^{5300 × 5 × 10}/₁₀₀

= ^{26500 × 10}/₁₀₀

= ²⁶⁵⁰⁰⁰/₁₀₀

= $2650

Thus, Simple Interest = $2650

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 = $5300 + $2650

= $7950

Thus, Amount to be paid = $7950 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 = $5300

Rate of Simple Interest (SI) or (R) = 5%

And, Time (t) = 10 years

Thus, Amount (A)

= $5300 + ($5300 × 5% × 10)

= $5300 + ($5300 ×⁵/₁₀₀ × 10)

= $5300 + (^{5300 × 5 × 10}/₁₀₀)

= $5300 + (^{26500 × 10}/₁₀₀)

= $5300 + (²⁶⁵⁰⁰⁰/₁₀₀)

= $5300 + $2650 = $7950

Thus, Amount (A) to be paid = $7950 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 5%

This, means, $5 per $100 per year

∵ For $100, the simple interest for 1 year = $5

∴ For $1, the simple interest for 1 year = ⁵/₁₀₀

∴ For $5300, the simple interest in 1 year

= ⁵/₁₀₀ × 5300

= ^{5 × 5300}/₁₀₀

= ²⁶⁵⁰⁰/₁₀₀ = $265

Thus, simple interest for 1 year = $265

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $265 × 10 = $2650

Thus, Simple Interest (SI) = $2650

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5300 + $2650

= $7950

Thus, Amount to be paid = $7950 Answer

Similar Questions

(1) How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?

(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.

(3) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.

(5) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.

(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.

(9) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.

(10) Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.