Simple Interest
Math MCQs

Question :    What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?

Correct Answer  $4312.5

Solution & Explanation

Solution

Given,

Principal (P) = $3450

Rate of Simple Interest (SI) = 5%

Time (t) = 5 years

Thus, Amount (A) = ?

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

Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 5

= $3450 ×⁵/₁₀₀ × 5

= ^{3450 × 5 × 5}/₁₀₀

= ^{17250 × 5}/₁₀₀

= ⁸⁶²⁵⁰/₁₀₀

= $862.5

Thus, Simple Interest = $862.5

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 + $862.5

= $4312.5

Thus, Amount to be paid = $4312.5 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) = 5%

And, Time (t) = 5 years

Thus, Amount (A)

= $3450 + ($3450 × 5% × 5)

= $3450 + ($3450 ×⁵/₁₀₀ × 5)

= $3450 + (^{3450 × 5 × 5}/₁₀₀)

= $3450 + (^{17250 × 5}/₁₀₀)

= $3450 + (⁸⁶²⁵⁰/₁₀₀)

= $3450 + $862.5 = $4312.5

Thus, Amount (A) to be paid = $4312.5 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 5%

This, means, $5 per $100 per year

∵ For $100, the simple interest for 1 year = $5

∴ For $1, the simple interest for 1 year = ⁵/₁₀₀

∴ For $3450, the simple interest in 1 year

= ⁵/₁₀₀ × 3450

= ^{5 × 3450}/₁₀₀

= ¹⁷²⁵⁰/₁₀₀ = $172.5

Thus, simple interest for 1 year = $172.5

Therefore, simple interest for 5 years

= Simple interest for 1 year × 5

= $172.5 × 5 = $862.5

Thus, Simple Interest (SI) = $862.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3450 + $862.5

= $4312.5

Thus, Amount to be paid = $4312.5 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.

(2) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.

(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?

(4) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.

(5) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?

(6) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.

(10) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.