Simple Interest
Math MCQs

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

Correct Answer  $8482.5

Solution & Explanation

Solution

Given,

Principal (P) = $5850

Rate of Simple Interest (SI) = 5%

Time (t) = 9 years

Thus, Amount (A) = ?

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

Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5850 × 5% × 9

= $5850 ×⁵/₁₀₀ × 9

= ^{5850 × 5 × 9}/₁₀₀

= ^{29250 × 9}/₁₀₀

= ²⁶³²⁵⁰/₁₀₀

= $2632.5

Thus, Simple Interest = $2632.5

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 = $5850 + $2632.5

= $8482.5

Thus, Amount to be paid = $8482.5 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 = $5850

Rate of Simple Interest (SI) or (R) = 5%

And, Time (t) = 9 years

Thus, Amount (A)

= $5850 + ($5850 × 5% × 9)

= $5850 + ($5850 ×⁵/₁₀₀ × 9)

= $5850 + (^{5850 × 5 × 9}/₁₀₀)

= $5850 + (^{29250 × 9}/₁₀₀)

= $5850 + (²⁶³²⁵⁰/₁₀₀)

= $5850 + $2632.5 = $8482.5

Thus, Amount (A) to be paid = $8482.5 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 5%

This, means, $5 per $100 per year

∵ For $100, the simple interest for 1 year = $5

∴ For $1, the simple interest for 1 year = ⁵/₁₀₀

∴ For $5850, the simple interest in 1 year

= ⁵/₁₀₀ × 5850

= ^{5 × 5850}/₁₀₀

= ²⁹²⁵⁰/₁₀₀ = $292.5

Thus, simple interest for 1 year = $292.5

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $292.5 × 9 = $2632.5

Thus, Simple Interest (SI) = $2632.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5850 + $2632.5

= $8482.5

Thus, Amount to be paid = $8482.5 Answer

Similar Questions

(1) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?

(2) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?

(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.

(4) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(5) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?

(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?

(7) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 3 years.

(9) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.