Simple Interest
Math MCQs

Question :    Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 8 years.

Correct Answer  $9890

Solution & Explanation

Solution

Given,

Principal (P) = $5750

Rate of Simple Interest (SI) = 9%

Time (t) = 8 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) = $5750 × 9% × 8

= $5750 ×⁹/₁₀₀ × 8

= ^{5750 × 9 × 8}/₁₀₀

= ^{51750 × 8}/₁₀₀

= ⁴¹⁴⁰⁰⁰/₁₀₀

= $4140

Thus, Simple Interest = $4140

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 = $5750 + $4140

= $9890

Thus, Amount to be paid = $9890 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 = $5750

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

And, Time (t) = 8 years

Thus, Amount (A)

= $5750 + ($5750 × 9% × 8)

= $5750 + ($5750 ×⁹/₁₀₀ × 8)

= $5750 + (^{5750 × 9 × 8}/₁₀₀)

= $5750 + (^{51750 × 8}/₁₀₀)

= $5750 + (⁴¹⁴⁰⁰⁰/₁₀₀)

= $5750 + $4140 = $9890

Thus, Amount (A) to be paid = $9890 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 $5750, the simple interest in 1 year

= ⁹/₁₀₀ × 5750

= ^{9 × 5750}/₁₀₀

= ⁵¹⁷⁵⁰/₁₀₀ = $517.5

Thus, simple interest for 1 year = $517.5

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $517.5 × 8 = $4140

Thus, Simple Interest (SI) = $4140

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5750 + $4140

= $9890

Thus, Amount to be paid = $9890 Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.

(3) If Jennifer paid $3900 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.

(5) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?

(7) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.

(8) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?

(9) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?