Simple Interest
Math MCQs

Question :    What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?

Correct Answer  $5313

Solution & Explanation

Solution

Given,

Principal (P) = $3450

Rate of Simple Interest (SI) = 9%

Time (t) = 6 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) = $3450 × 9% × 6

= $3450 ×⁹/₁₀₀ × 6

= ^{3450 × 9 × 6}/₁₀₀

= ^{31050 × 6}/₁₀₀

= ¹⁸⁶³⁰⁰/₁₀₀

= $1863

Thus, Simple Interest = $1863

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 + $1863

= $5313

Thus, Amount to be paid = $5313 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) = 9%

And, Time (t) = 6 years

Thus, Amount (A)

= $3450 + ($3450 × 9% × 6)

= $3450 + ($3450 ×⁹/₁₀₀ × 6)

= $3450 + (^{3450 × 9 × 6}/₁₀₀)

= $3450 + (^{31050 × 6}/₁₀₀)

= $3450 + (¹⁸⁶³⁰⁰/₁₀₀)

= $3450 + $1863 = $5313

Thus, Amount (A) to be paid = $5313 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 $3450, the simple interest in 1 year

= ⁹/₁₀₀ × 3450

= ^{9 × 3450}/₁₀₀

= ³¹⁰⁵⁰/₁₀₀ = $310.5

Thus, simple interest for 1 year = $310.5

Therefore, simple interest for 6 years

= Simple interest for 1 year × 6

= $310.5 × 6 = $1863

Thus, Simple Interest (SI) = $1863

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3450 + $1863

= $5313

Thus, Amount to be paid = $5313 Answer

Similar Questions

(1) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?

(2) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.

(5) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?

(6) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

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

(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.

(9) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?