Simple Interest
Math MCQs

Question :    What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?

Correct Answer  $4774

Solution & Explanation

Solution

Given,

Principal (P) = $3100

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) = $3100 × 9% × 6

= $3100 ×⁹/₁₀₀ × 6

= ^{3100 × 9 × 6}/₁₀₀

= ^{27900 × 6}/₁₀₀

= ¹⁶⁷⁴⁰⁰/₁₀₀

= $1674

Thus, Simple Interest = $1674

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 = $3100 + $1674

= $4774

Thus, Amount to be paid = $4774 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 = $3100

Rate of Simple Interest (SI) or (R) = 9%

And, Time (t) = 6 years

Thus, Amount (A)

= $3100 + ($3100 × 9% × 6)

= $3100 + ($3100 ×⁹/₁₀₀ × 6)

= $3100 + (^{3100 × 9 × 6}/₁₀₀)

= $3100 + (^{27900 × 6}/₁₀₀)

= $3100 + (¹⁶⁷⁴⁰⁰/₁₀₀)

= $3100 + $1674 = $4774

Thus, Amount (A) to be paid = $4774 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 $3100, the simple interest in 1 year

= ⁹/₁₀₀ × 3100

= ^{9 × 3100}/₁₀₀

= ²⁷⁹⁰⁰/₁₀₀ = $279

Thus, simple interest for 1 year = $279

Therefore, simple interest for 6 years

= Simple interest for 1 year × 6

= $279 × 6 = $1674

Thus, Simple Interest (SI) = $1674

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3100 + $1674

= $4774

Thus, Amount to be paid = $4774 Answer

Similar Questions

(1) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.

(2) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?

(3) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?

(4) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?

(5) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.

(6) If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?

(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.

(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?

(10) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.