Simple Interest
Math MCQs

Question :    What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 10% simple interest?

Correct Answer  $4725

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (SI) = 10%

Time (t) = 5 years

Thus, Amount (A) = ?

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

Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $3150 × 10% × 5

= $3150 ×¹⁰/₁₀₀ × 5

= ^{3150 × 10 × 5}/₁₀₀

= ^{31500 × 5}/₁₀₀

= ¹⁵⁷⁵⁰⁰/₁₀₀

= $1575

Thus, Simple Interest = $1575

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 = $3150 + $1575

= $4725

Thus, Amount to be paid = $4725 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 = $3150

Rate of Simple Interest (SI) or (R) = 10%

And, Time (t) = 5 years

Thus, Amount (A)

= $3150 + ($3150 × 10% × 5)

= $3150 + ($3150 ×¹⁰/₁₀₀ × 5)

= $3150 + (^{3150 × 10 × 5}/₁₀₀)

= $3150 + (^{31500 × 5}/₁₀₀)

= $3150 + (¹⁵⁷⁵⁰⁰/₁₀₀)

= $3150 + $1575 = $4725

Thus, Amount (A) to be paid = $4725 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 10%

This, means, $10 per $100 per year

∵ For $100, the simple interest for 1 year = $10

∴ For $1, the simple interest for 1 year = ¹⁰/₁₀₀

∴ For $3150, the simple interest in 1 year

= ¹⁰/₁₀₀ × 3150

= ^{10 × 3150}/₁₀₀

= ³¹⁵⁰⁰/₁₀₀ = $315

Thus, simple interest for 1 year = $315

Therefore, simple interest for 5 years

= Simple interest for 1 year × 5

= $315 × 5 = $1575

Thus, Simple Interest (SI) = $1575

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3150 + $1575

= $4725

Thus, Amount to be paid = $4725 Answer

Similar Questions

(1) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.

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

(4) How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?

(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 6% simple interest?

(6) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(7) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 4 years.

(9) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.

(10) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?