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) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.

(3) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.

(5) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?

(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.

(8) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.

(9) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.

(10) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.