Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.

Correct Answer  $10165

Solution & Explanation

Solution

Given,

Principal (P) = $5350

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) = $5350 × 9% × 10

= $5350 ×⁹/₁₀₀ × 10

= ^{5350 × 9 × 10}/₁₀₀

= ^{48150 × 10}/₁₀₀

= ⁴⁸¹⁵⁰⁰/₁₀₀

= $4815

Thus, Simple Interest = $4815

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 = $5350 + $4815

= $10165

Thus, Amount to be paid = $10165 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 = $5350

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

And, Time (t) = 10 years

Thus, Amount (A)

= $5350 + ($5350 × 9% × 10)

= $5350 + ($5350 ×⁹/₁₀₀ × 10)

= $5350 + (^{5350 × 9 × 10}/₁₀₀)

= $5350 + (^{48150 × 10}/₁₀₀)

= $5350 + (⁴⁸¹⁵⁰⁰/₁₀₀)

= $5350 + $4815 = $10165

Thus, Amount (A) to be paid = $10165 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 $5350, the simple interest in 1 year

= ⁹/₁₀₀ × 5350

= ^{9 × 5350}/₁₀₀

= ⁴⁸¹⁵⁰/₁₀₀ = $481.5

Thus, simple interest for 1 year = $481.5

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $481.5 × 10 = $4815

Thus, Simple Interest (SI) = $4815

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5350 + $4815

= $10165

Thus, Amount to be paid = $10165 Answer

Similar Questions

(1) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(2) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(3) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?

(4) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.

(6) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.

(7) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?

(8) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.

(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.