Simple Interest
Math MCQs

Question :    What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?

Correct Answer  $4851

Solution & Explanation

Solution

Given,

Principal (P) = $3150

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) = $3150 × 9% × 6

= $3150 ×⁹/₁₀₀ × 6

= ^{3150 × 9 × 6}/₁₀₀

= ^{28350 × 6}/₁₀₀

= ¹⁷⁰¹⁰⁰/₁₀₀

= $1701

Thus, Simple Interest = $1701

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 + $1701

= $4851

Thus, Amount to be paid = $4851 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) = 9%

And, Time (t) = 6 years

Thus, Amount (A)

= $3150 + ($3150 × 9% × 6)

= $3150 + ($3150 ×⁹/₁₀₀ × 6)

= $3150 + (^{3150 × 9 × 6}/₁₀₀)

= $3150 + (^{28350 × 6}/₁₀₀)

= $3150 + (¹⁷⁰¹⁰⁰/₁₀₀)

= $3150 + $1701 = $4851

Thus, Amount (A) to be paid = $4851 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 $3150, the simple interest in 1 year

= ⁹/₁₀₀ × 3150

= ^{9 × 3150}/₁₀₀

= ²⁸³⁵⁰/₁₀₀ = $283.5

Thus, simple interest for 1 year = $283.5

Therefore, simple interest for 6 years

= Simple interest for 1 year × 6

= $283.5 × 6 = $1701

Thus, Simple Interest (SI) = $1701

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3150 + $1701

= $4851

Thus, Amount to be paid = $4851 Answer

Similar Questions

(1) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.

(2) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.

(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.

(5) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) If Linda borrowed $3350 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.

(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 2% simple interest?

(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.

(10) If John paid $3456 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.