Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.

Correct Answer  $8720

Solution & Explanation

Solution

Given,

Principal (P) = $5450

Rate of Simple Interest (SI) = 6%

Time (t) = 10 years

Thus, Amount (A) = ?

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

Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5450 × 6% × 10

= $5450 ×⁶/₁₀₀ × 10

= ^{5450 × 6 × 10}/₁₀₀

= ^{32700 × 10}/₁₀₀

= ³²⁷⁰⁰⁰/₁₀₀

= $3270

Thus, Simple Interest = $3270

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 = $5450 + $3270

= $8720

Thus, Amount to be paid = $8720 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 = $5450

Rate of Simple Interest (SI) or (R) = 6%

And, Time (t) = 10 years

Thus, Amount (A)

= $5450 + ($5450 × 6% × 10)

= $5450 + ($5450 ×⁶/₁₀₀ × 10)

= $5450 + (^{5450 × 6 × 10}/₁₀₀)

= $5450 + (^{32700 × 10}/₁₀₀)

= $5450 + (³²⁷⁰⁰⁰/₁₀₀)

= $5450 + $3270 = $8720

Thus, Amount (A) to be paid = $8720 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 6%

This, means, $6 per $100 per year

∵ For $100, the simple interest for 1 year = $6

∴ For $1, the simple interest for 1 year = ⁶/₁₀₀

∴ For $5450, the simple interest in 1 year

= ⁶/₁₀₀ × 5450

= ^{6 × 5450}/₁₀₀

= ³²⁷⁰⁰/₁₀₀ = $327

Thus, simple interest for 1 year = $327

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $327 × 10 = $3270

Thus, Simple Interest (SI) = $3270

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5450 + $3270

= $8720

Thus, Amount to be paid = $8720 Answer

Similar Questions

(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.

(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.

(3) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.

(4) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?

(5) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.

(6) Kimberly had to pay $5347.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?

(8) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.

(9) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?

(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 2% simple interest?