Simple Interest
Math MCQs

Question :  ( 1 of 10 )  Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.

Correct Answer  $7752

Solution & Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (SI) = 4%

Time (t) = 9 years

Thus, Amount (A) = ?

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

Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 9

= $5700 ×⁴/₁₀₀ × 9

= ^{5700 × 4 × 9}/₁₀₀

= ^{22800 × 9}/₁₀₀

= ²⁰⁵²⁰⁰/₁₀₀

= $2052

Thus, Simple Interest = $2052

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 + $2052

= $7752

Thus, Amount to be paid = $7752 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) = 4%

And, Time (t) = 9 years

Thus, Amount (A)

= $5700 + ($5700 × 4% × 9)

= $5700 + ($5700 ×⁴/₁₀₀ × 9)

= $5700 + (^{5700 × 4 × 9}/₁₀₀)

= $5700 + (^{22800 × 9}/₁₀₀)

= $5700 + (²⁰⁵²⁰⁰/₁₀₀)

= $5700 + $2052 = $7752

Thus, Amount (A) to be paid = $7752 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 4%

This, means, $4 per $100 per year

∵ For $100, the simple interest for 1 year = $4

∴ For $1, the simple interest for 1 year = ⁴/₁₀₀

∴ For $5700, the simple interest in 1 year

= ⁴/₁₀₀ × 5700

= ^{4 × 5700}/₁₀₀

= ²²⁸⁰⁰/₁₀₀ = $228

Thus, simple interest for 1 year = $228

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $228 × 9 = $2052

Thus, Simple Interest (SI) = $2052

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5700 + $2052

= $7752

Thus, Amount to be paid = $7752 Answer

Similar Questions

(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.

(2) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?

(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.

(4) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(6) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?

(8) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?

(9) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.

(10) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.