Simple Interest
Math MCQs

Question :    What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?

Correct Answer  $4495

Solution & Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (SI) = 9%

Time (t) = 5 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) = $3100 × 9% × 5

= $3100 ×⁹/₁₀₀ × 5

= ^{3100 × 9 × 5}/₁₀₀

= ^{27900 × 5}/₁₀₀

= ¹³⁹⁵⁰⁰/₁₀₀

= $1395

Thus, Simple Interest = $1395

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 = $3100 + $1395

= $4495

Thus, Amount to be paid = $4495 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 = $3100

Rate of Simple Interest (SI) or (R) = 9%

And, Time (t) = 5 years

Thus, Amount (A)

= $3100 + ($3100 × 9% × 5)

= $3100 + ($3100 ×⁹/₁₀₀ × 5)

= $3100 + (^{3100 × 9 × 5}/₁₀₀)

= $3100 + (^{27900 × 5}/₁₀₀)

= $3100 + (¹³⁹⁵⁰⁰/₁₀₀)

= $3100 + $1395 = $4495

Thus, Amount (A) to be paid = $4495 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 $3100, the simple interest in 1 year

= ⁹/₁₀₀ × 3100

= ^{9 × 3100}/₁₀₀

= ²⁷⁹⁰⁰/₁₀₀ = $279

Thus, simple interest for 1 year = $279

Therefore, simple interest for 5 years

= Simple interest for 1 year × 5

= $279 × 5 = $1395

Thus, Simple Interest (SI) = $1395

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3100 + $1395

= $4495

Thus, Amount to be paid = $4495 Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(2) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?

(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.

(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.

(5) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

(7) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(8) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(10) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.