Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.

Correct Answer  $10830

Solution & Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (SI) = 9%

Time (t) = 10 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) = $5700 × 9% × 10

= $5700 ×⁹/₁₀₀ × 10

= ^{5700 × 9 × 10}/₁₀₀

= ^{51300 × 10}/₁₀₀

= ⁵¹³⁰⁰⁰/₁₀₀

= $5130

Thus, Simple Interest = $5130

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 = $5700 + $5130

= $10830

Thus, Amount to be paid = $10830 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 = $5700

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

And, Time (t) = 10 years

Thus, Amount (A)

= $5700 + ($5700 × 9% × 10)

= $5700 + ($5700 ×⁹/₁₀₀ × 10)

= $5700 + (^{5700 × 9 × 10}/₁₀₀)

= $5700 + (^{51300 × 10}/₁₀₀)

= $5700 + (⁵¹³⁰⁰⁰/₁₀₀)

= $5700 + $5130 = $10830

Thus, Amount (A) to be paid = $10830 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 $5700, the simple interest in 1 year

= ⁹/₁₀₀ × 5700

= ^{9 × 5700}/₁₀₀

= ⁵¹³⁰⁰/₁₀₀ = $513

Thus, simple interest for 1 year = $513

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $513 × 10 = $5130

Thus, Simple Interest (SI) = $5130

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5700 + $5130

= $10830

Thus, Amount to be paid = $10830 Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.

(3) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?

(4) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?

(5) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?

(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.

(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?

(8) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?

(9) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.

(10) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.