Simple Interest
Math MCQs

Question :    What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?

Correct Answer  $4828

Solution & Explanation

Solution

Given,

Principal (P) = $3400

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) = $3400 × 7% × 6

= $3400 ×⁷/₁₀₀ × 6

= ^{3400 × 7 × 6}/₁₀₀

= ^{23800 × 6}/₁₀₀

= ¹⁴²⁸⁰⁰/₁₀₀

= $1428

Thus, Simple Interest = $1428

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 = $3400 + $1428

= $4828

Thus, Amount to be paid = $4828 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 = $3400

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

And, Time (t) = 6 years

Thus, Amount (A)

= $3400 + ($3400 × 7% × 6)

= $3400 + ($3400 ×⁷/₁₀₀ × 6)

= $3400 + (^{3400 × 7 × 6}/₁₀₀)

= $3400 + (^{23800 × 6}/₁₀₀)

= $3400 + (¹⁴²⁸⁰⁰/₁₀₀)

= $3400 + $1428 = $4828

Thus, Amount (A) to be paid = $4828 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 $3400, the simple interest in 1 year

= ⁷/₁₀₀ × 3400

= ^{7 × 3400}/₁₀₀

= ²³⁸⁰⁰/₁₀₀ = $238

Thus, simple interest for 1 year = $238

Therefore, simple interest for 6 years

= Simple interest for 1 year × 6

= $238 × 6 = $1428

Thus, Simple Interest (SI) = $1428

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3400 + $1428

= $4828

Thus, Amount to be paid = $4828 Answer

Similar Questions

(1) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?

(2) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.

(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.

(4) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?

(5) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?

(6) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.

(8) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.

(9) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(10) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.