Simple Interest
Math MCQs

Question :    Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.

Correct Answer  $8755

Solution & Explanation

Solution

Given,

Principal (P) = $5150

Rate of Simple Interest (SI) = 10%

Time (t) = 7 years

Thus, Amount (A) = ?

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

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

= $5150 ×¹⁰/₁₀₀ × 7

= ^{5150 × 10 × 7}/₁₀₀

= ^{51500 × 7}/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) = 10%

And, Time (t) = 7 years

Thus, Amount (A)

= $5150 + ($5150 × 10% × 7)

= $5150 + ($5150 ×¹⁰/₁₀₀ × 7)

= $5150 + (^{5150 × 10 × 7}/₁₀₀)

= $5150 + (^{51500 × 7}/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 = 10%

This, means, $10 per $100 per year

∵ For $100, the simple interest for 1 year = $10

∴ For $1, the simple interest for 1 year = ¹⁰/₁₀₀

∴ For $5150, the simple interest in 1 year

= ¹⁰/₁₀₀ × 5150

= ^{10 × 5150}/₁₀₀

= ⁵¹⁵⁰⁰/₁₀₀ = $515

Thus, simple interest for 1 year = $515

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $515 × 7 = $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) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?

(2) How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?

(3) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.

(4) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?

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

(6) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 8 years.

(8) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.

(9) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

(10) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.