Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.

Correct Answer  $8755

Solution & Explanation

Solution

Given,

Principal (P) = $5150

Rate of Simple Interest (SI) = 7%

Time (t) = 10 years

Thus, Amount (A) = ?

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

Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 10

= $5150 ×⁷/₁₀₀ × 10

= ^{5150 × 7 × 10}/₁₀₀

= ^{36050 × 10}/₁₀₀

= ³⁶⁰⁵⁰⁰/₁₀₀

= $3605

Thus, Simple Interest = $3605

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 + $3605

= $8755

Thus, Amount to be paid = $8755 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) = 7%

And, Time (t) = 10 years

Thus, Amount (A)

= $5150 + ($5150 × 7% × 10)

= $5150 + ($5150 ×⁷/₁₀₀ × 10)

= $5150 + (^{5150 × 7 × 10}/₁₀₀)

= $5150 + (^{36050 × 10}/₁₀₀)

= $5150 + (³⁶⁰⁵⁰⁰/₁₀₀)

= $5150 + $3605 = $8755

Thus, Amount (A) to be paid = $8755 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 7%

This, means, $7 per $100 per year

∵ For $100, the simple interest for 1 year = $7

∴ For $1, the simple interest for 1 year = ⁷/₁₀₀

∴ For $5150, the simple interest in 1 year

= ⁷/₁₀₀ × 5150

= ^{7 × 5150}/₁₀₀

= ³⁶⁰⁵⁰/₁₀₀ = $360.5

Thus, simple interest for 1 year = $360.5

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $360.5 × 10 = $3605

Thus, Simple Interest (SI) = $3605

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5150 + $3605

= $8755

Thus, Amount to be paid = $8755 Answer

Similar Questions

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

(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.

(3) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 7 years.

(6) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?

(7) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.

(8) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.

(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?

(10) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.