Simple Interest
Math MCQs

Question :    What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?

Correct Answer  $4650

Solution & Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (SI) = 10%

Time (t) = 5 years

Thus, Amount (A) = ?

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

Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $3100 × 10% × 5

= $3100 ×¹⁰/₁₀₀ × 5

= ^{3100 × 10 × 5}/₁₀₀

= ^{31000 × 5}/₁₀₀

= ¹⁵⁵⁰⁰⁰/₁₀₀

= $1550

Thus, Simple Interest = $1550

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 = $3100 + $1550

= $4650

Thus, Amount to be paid = $4650 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 = $3100

Rate of Simple Interest (SI) or (R) = 10%

And, Time (t) = 5 years

Thus, Amount (A)

= $3100 + ($3100 × 10% × 5)

= $3100 + ($3100 ×¹⁰/₁₀₀ × 5)

= $3100 + (^{3100 × 10 × 5}/₁₀₀)

= $3100 + (^{31000 × 5}/₁₀₀)

= $3100 + (¹⁵⁵⁰⁰⁰/₁₀₀)

= $3100 + $1550 = $4650

Thus, Amount (A) to be paid = $4650 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 10%

This, means, $10 per $100 per year

∵ For $100, the simple interest for 1 year = $10

∴ For $1, the simple interest for 1 year = ¹⁰/₁₀₀

∴ For $3100, the simple interest in 1 year

= ¹⁰/₁₀₀ × 3100

= ^{10 × 3100}/₁₀₀

= ³¹⁰⁰⁰/₁₀₀ = $310

Thus, simple interest for 1 year = $310

Therefore, simple interest for 5 years

= Simple interest for 1 year × 5

= $310 × 5 = $1550

Thus, Simple Interest (SI) = $1550

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3100 + $1550

= $4650

Thus, Amount to be paid = $4650 Answer

Similar Questions

(1) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.

(2) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.

(3) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(4) If Steven paid $5152 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 8 years.

(6) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.

(7) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 4 years.

(8) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(9) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.