Simple Interest
Math MCQs

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

Correct Answer  $6952.5

Solution & Explanation

Solution

Given,

Principal (P) = $5150

Rate of Simple Interest (SI) = 5%

Time (t) = 7 years

Thus, Amount (A) = ?

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

Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 7

= $5150 ×⁵/₁₀₀ × 7

= ^{5150 × 5 × 7}/₁₀₀

= ^{25750 × 7}/₁₀₀

= ¹⁸⁰²⁵⁰/₁₀₀

= $1802.5

Thus, Simple Interest = $1802.5

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 + $1802.5

= $6952.5

Thus, Amount to be paid = $6952.5 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) = 5%

And, Time (t) = 7 years

Thus, Amount (A)

= $5150 + ($5150 × 5% × 7)

= $5150 + ($5150 ×⁵/₁₀₀ × 7)

= $5150 + (^{5150 × 5 × 7}/₁₀₀)

= $5150 + (^{25750 × 7}/₁₀₀)

= $5150 + (¹⁸⁰²⁵⁰/₁₀₀)

= $5150 + $1802.5 = $6952.5

Thus, Amount (A) to be paid = $6952.5 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 5%

This, means, $5 per $100 per year

∵ For $100, the simple interest for 1 year = $5

∴ For $1, the simple interest for 1 year = ⁵/₁₀₀

∴ For $5150, the simple interest in 1 year

= ⁵/₁₀₀ × 5150

= ^{5 × 5150}/₁₀₀

= ²⁵⁷⁵⁰/₁₀₀ = $257.5

Thus, simple interest for 1 year = $257.5

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $257.5 × 7 = $1802.5

Thus, Simple Interest (SI) = $1802.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5150 + $1802.5

= $6952.5

Thus, Amount to be paid = $6952.5 Answer

Similar Questions

(1) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 5% simple interest?

(4) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?

(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.

(6) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.

(7) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.

(8) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?

(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.

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