Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.

Correct Answer  $8858

Solution & Explanation

Solution

Given,

Principal (P) = $5150

Rate of Simple Interest (SI) = 8%

Time (t) = 9 years

Thus, Amount (A) = ?

The Rate of Interest is always calculated per annum, i.e. per year.

Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 9

= $5150 ×⁸/₁₀₀ × 9

= ^{5150 × 8 × 9}/₁₀₀

= ^{41200 × 9}/₁₀₀

= ³⁷⁰⁸⁰⁰/₁₀₀

= $3708

Thus, Simple Interest = $3708

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 + $3708

= $8858

Thus, Amount to be paid = $8858 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) = 8%

And, Time (t) = 9 years

Thus, Amount (A)

= $5150 + ($5150 × 8% × 9)

= $5150 + ($5150 ×⁸/₁₀₀ × 9)

= $5150 + (^{5150 × 8 × 9}/₁₀₀)

= $5150 + (^{41200 × 9}/₁₀₀)

= $5150 + (³⁷⁰⁸⁰⁰/₁₀₀)

= $5150 + $3708 = $8858

Thus, Amount (A) to be paid = $8858 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 8%

This, means, $8 per $100 per year

∵ For $100, the simple interest for 1 year = $8

∴ For $1, the simple interest for 1 year = ⁸/₁₀₀

∴ For $5150, the simple interest in 1 year

= ⁸/₁₀₀ × 5150

= ^{8 × 5150}/₁₀₀

= ⁴¹²⁰⁰/₁₀₀ = $412

Thus, simple interest for 1 year = $412

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $412 × 9 = $3708

Thus, Simple Interest (SI) = $3708

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5150 + $3708

= $8858

Thus, Amount to be paid = $8858 Answer

Similar Questions

(1) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(4) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 3 years.

(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?

(6) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 3 years.

(8) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?

(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?