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) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.

(2) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.

(3) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?

(4) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.

(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.

(6) How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?

(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.

(8) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?

(9) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?

(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.