Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.

Correct Answer  $8080

Solution & Explanation

Solution

Given,

Principal (P) = $5050

Rate of Simple Interest (SI) = 6%

Time (t) = 10 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) = $5050 × 6% × 10

= $5050 ×⁶/₁₀₀ × 10

= ^{5050 × 6 × 10}/₁₀₀

= ^{30300 × 10}/₁₀₀

= ³⁰³⁰⁰⁰/₁₀₀

= $3030

Thus, Simple Interest = $3030

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 = $5050 + $3030

= $8080

Thus, Amount to be paid = $8080 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 = $5050

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

And, Time (t) = 10 years

Thus, Amount (A)

= $5050 + ($5050 × 6% × 10)

= $5050 + ($5050 ×⁶/₁₀₀ × 10)

= $5050 + (^{5050 × 6 × 10}/₁₀₀)

= $5050 + (^{30300 × 10}/₁₀₀)

= $5050 + (³⁰³⁰⁰⁰/₁₀₀)

= $5050 + $3030 = $8080

Thus, Amount (A) to be paid = $8080 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 $5050, the simple interest in 1 year

= ⁶/₁₀₀ × 5050

= ^{6 × 5050}/₁₀₀

= ³⁰³⁰⁰/₁₀₀ = $303

Thus, simple interest for 1 year = $303

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $303 × 10 = $3030

Thus, Simple Interest (SI) = $3030

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5050 + $3030

= $8080

Thus, Amount to be paid = $8080 Answer

Similar Questions

(1) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 7% simple interest?

(2) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?

(3) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?

(4) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?

(5) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.

(6) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.

(9) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.