Simple Interest
Math MCQs

Question :    If Elizabeth borrowed $3450 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

Correct Answer  $3657

Solution & Explanation

Solution

Given,

Principal (P) = $3450

Rate of Simple Interest (SI) = 3%

Time (t) = 2 years

Thus, Amount (A) = ?

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

Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $3450 × 3% × 2

= $3450 ׳/₁₀₀ × 2

= ^{3450 × 3 × 2}/₁₀₀

= ^{10350 × 2}/₁₀₀

= ²⁰⁷⁰⁰/₁₀₀

= $207

Thus, Simple Interest = $207

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 = $3450 + $207

= $3657

Thus, Amount to be paid = $3657 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 = $3450

Rate of Simple Interest (SI) or (R) = 3%

And, Time (t) = 2 years

Thus, Amount (A)

= $3450 + ($3450 × 3% × 2)

= $3450 + ($3450 ׳/₁₀₀ × 2)

= $3450 + (^{3450 × 3 × 2}/₁₀₀)

= $3450 + (^{10350 × 2}/₁₀₀)

= $3450 + (²⁰⁷⁰⁰/₁₀₀)

= $3450 + $207 = $3657

Thus, Amount (A) to be paid = $3657 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 3%

This, means, $3 per $100 per year

∵ For $100, the simple interest for 1 year = $3

∴ For $1, the simple interest for 1 year = ³/₁₀₀

∴ For $3450, the simple interest in 1 year

= ³/₁₀₀ × 3450

= ^{3 × 3450}/₁₀₀

= ¹⁰³⁵⁰/₁₀₀ = $103.5

Thus, simple interest for 1 year = $103.5

Therefore, simple interest for 2 years

= Simple interest for 1 year × 2

= $103.5 × 2 = $207

Thus, Simple Interest (SI) = $207

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3450 + $207

= $3657

Thus, Amount to be paid = $3657 Answer

Similar Questions

(1) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?

(2) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.

(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?

(4) How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?

(5) How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?

(6) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 10% simple interest?

(7) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(8) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

(9) If Sandra paid $4806 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.