Simple Interest
Math MCQs

Question :    What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?

Correct Answer  $5265

Solution & Explanation

Solution

Given,

Principal (P) = $3900

Rate of Simple Interest (SI) = 7%

Time (t) = 5 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) = $3900 × 7% × 5

= $3900 ×⁷/₁₀₀ × 5

= ^{3900 × 7 × 5}/₁₀₀

= ^{27300 × 5}/₁₀₀

= ¹³⁶⁵⁰⁰/₁₀₀

= $1365

Thus, Simple Interest = $1365

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 + $1365

= $5265

Thus, Amount to be paid = $5265 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) = 7%

And, Time (t) = 5 years

Thus, Amount (A)

= $3900 + ($3900 × 7% × 5)

= $3900 + ($3900 ×⁷/₁₀₀ × 5)

= $3900 + (^{3900 × 7 × 5}/₁₀₀)

= $3900 + (^{27300 × 5}/₁₀₀)

= $3900 + (¹³⁶⁵⁰⁰/₁₀₀)

= $3900 + $1365 = $5265

Thus, Amount (A) to be paid = $5265 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 $3900, the simple interest in 1 year

= ⁷/₁₀₀ × 3900

= ^{7 × 3900}/₁₀₀

= ²⁷³⁰⁰/₁₀₀ = $273

Thus, simple interest for 1 year = $273

Therefore, simple interest for 5 years

= Simple interest for 1 year × 5

= $273 × 5 = $1365

Thus, Simple Interest (SI) = $1365

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3900 + $1365

= $5265

Thus, Amount to be paid = $5265 Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.

(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.

(4) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.

(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.

(7) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.

(8) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?

(9) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?

(10) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.