Simple Interest
Math MCQs

Question :    What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?

Correct Answer  $5460

Solution & Explanation

Solution

Given,

Principal (P) = $3900

Rate of Simple Interest (SI) = 8%

Time (t) = 5 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) = $3900 × 8% × 5

= $3900 ×⁸/₁₀₀ × 5

= ^{3900 × 8 × 5}/₁₀₀

= ^{31200 × 5}/₁₀₀

= ¹⁵⁶⁰⁰⁰/₁₀₀

= $1560

Thus, Simple Interest = $1560

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 = $3900 + $1560

= $5460

Thus, Amount to be paid = $5460 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 = $3900

Rate of Simple Interest (SI) or (R) = 8%

And, Time (t) = 5 years

Thus, Amount (A)

= $3900 + ($3900 × 8% × 5)

= $3900 + ($3900 ×⁸/₁₀₀ × 5)

= $3900 + (^{3900 × 8 × 5}/₁₀₀)

= $3900 + (^{31200 × 5}/₁₀₀)

= $3900 + (¹⁵⁶⁰⁰⁰/₁₀₀)

= $3900 + $1560 = $5460

Thus, Amount (A) to be paid = $5460 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 $3900, the simple interest in 1 year

= ⁸/₁₀₀ × 3900

= ^{8 × 3900}/₁₀₀

= ³¹²⁰⁰/₁₀₀ = $312

Thus, simple interest for 1 year = $312

Therefore, simple interest for 5 years

= Simple interest for 1 year × 5

= $312 × 5 = $1560

Thus, Simple Interest (SI) = $1560

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3900 + $1560

= $5460

Thus, Amount to be paid = $5460 Answer

Similar Questions

(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?

(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?

(3) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.

(4) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.

(5) Lisa had to pay $4293 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(7) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(8) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?

(10) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.