Simple Interest
Math MCQs

Question :    What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?

Correct Answer  $5680

Solution & Explanation

Solution

Given,

Principal (P) = $4000

Rate of Simple Interest (SI) = 7%

Time (t) = 6 years

Thus, Amount (A) = ?

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

Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $4000 × 7% × 6

= $4000 ×⁷/₁₀₀ × 6

= ^{4000 × 7 × 6}/₁₀₀

= ^{28000 × 6}/₁₀₀

= ¹⁶⁸⁰⁰⁰/₁₀₀

= $1680

Thus, Simple Interest = $1680

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 = $4000 + $1680

= $5680

Thus, Amount to be paid = $5680 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 = $4000

Rate of Simple Interest (SI) or (R) = 7%

And, Time (t) = 6 years

Thus, Amount (A)

= $4000 + ($4000 × 7% × 6)

= $4000 + ($4000 ×⁷/₁₀₀ × 6)

= $4000 + (^{4000 × 7 × 6}/₁₀₀)

= $4000 + (^{28000 × 6}/₁₀₀)

= $4000 + (¹⁶⁸⁰⁰⁰/₁₀₀)

= $4000 + $1680 = $5680

Thus, Amount (A) to be paid = $5680 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 7%

This, means, $7 per $100 per year

∵ For $100, the simple interest for 1 year = $7

∴ For $1, the simple interest for 1 year = ⁷/₁₀₀

∴ For $4000, the simple interest in 1 year

= ⁷/₁₀₀ × 4000

= ^{7 × 4000}/₁₀₀

= ²⁸⁰⁰⁰/₁₀₀ = $280

Thus, simple interest for 1 year = $280

Therefore, simple interest for 6 years

= Simple interest for 1 year × 6

= $280 × 6 = $1680

Thus, Simple Interest (SI) = $1680

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $4000 + $1680

= $5680

Thus, Amount to be paid = $5680 Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.

(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.

(4) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.

(5) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?

(6) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 4 years.

(7) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 3 years.

(8) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(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) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.