Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.

Correct Answer  $9785

Solution & Explanation

Solution

Given,

Principal (P) = $5150

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) = $5150 × 9% × 10

= $5150 ×⁹/₁₀₀ × 10

= ^{5150 × 9 × 10}/₁₀₀

= ^{46350 × 10}/₁₀₀

= ⁴⁶³⁵⁰⁰/₁₀₀

= $4635

Thus, Simple Interest = $4635

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 = $5150 + $4635

= $9785

Thus, Amount to be paid = $9785 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 = $5150

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

And, Time (t) = 10 years

Thus, Amount (A)

= $5150 + ($5150 × 9% × 10)

= $5150 + ($5150 ×⁹/₁₀₀ × 10)

= $5150 + (^{5150 × 9 × 10}/₁₀₀)

= $5150 + (^{46350 × 10}/₁₀₀)

= $5150 + (⁴⁶³⁵⁰⁰/₁₀₀)

= $5150 + $4635 = $9785

Thus, Amount (A) to be paid = $9785 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 $5150, the simple interest in 1 year

= ⁹/₁₀₀ × 5150

= ^{9 × 5150}/₁₀₀

= ⁴⁶³⁵⁰/₁₀₀ = $463.5

Thus, simple interest for 1 year = $463.5

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $463.5 × 10 = $4635

Thus, Simple Interest (SI) = $4635

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5150 + $4635

= $9785

Thus, Amount to be paid = $9785 Answer

Similar Questions

(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.

(2) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?

(3) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 4 years.

(5) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 8% simple interest?

(7) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.

(9) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.

(10) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.