Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.

Correct Answer  $11115

Solution & Explanation

Solution

Given,

Principal (P) = $5850

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) = $5850 × 9% × 10

= $5850 ×⁹/₁₀₀ × 10

= ^{5850 × 9 × 10}/₁₀₀

= ^{52650 × 10}/₁₀₀

= ⁵²⁶⁵⁰⁰/₁₀₀

= $5265

Thus, Simple Interest = $5265

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 + $5265

= $11115

Thus, Amount to be paid = $11115 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) = 9%

And, Time (t) = 10 years

Thus, Amount (A)

= $5850 + ($5850 × 9% × 10)

= $5850 + ($5850 ×⁹/₁₀₀ × 10)

= $5850 + (^{5850 × 9 × 10}/₁₀₀)

= $5850 + (^{52650 × 10}/₁₀₀)

= $5850 + (⁵²⁶⁵⁰⁰/₁₀₀)

= $5850 + $5265 = $11115

Thus, Amount (A) to be paid = $11115 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 $5850, the simple interest in 1 year

= ⁹/₁₀₀ × 5850

= ^{9 × 5850}/₁₀₀

= ⁵²⁶⁵⁰/₁₀₀ = $526.5

Thus, simple interest for 1 year = $526.5

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $526.5 × 10 = $5265

Thus, Simple Interest (SI) = $5265

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5850 + $5265

= $11115

Thus, Amount to be paid = $11115 Answer

Similar Questions

(1) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.

(2) If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?

(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.

(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?

(6) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.

(8) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?

(10) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.