Simple Interest
Math MCQs

Question :    What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?

Correct Answer  $6006

Solution & Explanation

Solution

Given,

Principal (P) = $3900

Rate of Simple Interest (SI) = 9%

Time (t) = 6 years

Thus, Amount (A) = ?

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

Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 6

= $3900 ×⁹/₁₀₀ × 6

= ^{3900 × 9 × 6}/₁₀₀

= ^{35100 × 6}/₁₀₀

= ²¹⁰⁶⁰⁰/₁₀₀

= $2106

Thus, Simple Interest = $2106

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 + $2106

= $6006

Thus, Amount to be paid = $6006 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) = 9%

And, Time (t) = 6 years

Thus, Amount (A)

= $3900 + ($3900 × 9% × 6)

= $3900 + ($3900 ×⁹/₁₀₀ × 6)

= $3900 + (^{3900 × 9 × 6}/₁₀₀)

= $3900 + (^{35100 × 6}/₁₀₀)

= $3900 + (²¹⁰⁶⁰⁰/₁₀₀)

= $3900 + $2106 = $6006

Thus, Amount (A) to be paid = $6006 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 9%

This, means, $9 per $100 per year

∵ For $100, the simple interest for 1 year = $9

∴ For $1, the simple interest for 1 year = ⁹/₁₀₀

∴ For $3900, the simple interest in 1 year

= ⁹/₁₀₀ × 3900

= ^{9 × 3900}/₁₀₀

= ³⁵¹⁰⁰/₁₀₀ = $351

Thus, simple interest for 1 year = $351

Therefore, simple interest for 6 years

= Simple interest for 1 year × 6

= $351 × 6 = $2106

Thus, Simple Interest (SI) = $2106

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3900 + $2106

= $6006

Thus, Amount to be paid = $6006 Answer

Similar Questions

(1) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

(2) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.

(3) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?

(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.

(5) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.

(6) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 4 years.

(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.

(9) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?

(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.