Simple Interest
Math MCQs

Question :    Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.

Correct Answer  $9698.5

Solution & Explanation

Solution

Given,

Principal (P) = $5950

Rate of Simple Interest (SI) = 9%

Time (t) = 7 years

Thus, Amount (A) = ?

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

Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $5950 × 9% × 7

= $5950 ×⁹/₁₀₀ × 7

= ^{5950 × 9 × 7}/₁₀₀

= ^{53550 × 7}/₁₀₀

= ³⁷⁴⁸⁵⁰/₁₀₀

= $3748.5

Thus, Simple Interest = $3748.5

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 = $5950 + $3748.5

= $9698.5

Thus, Amount to be paid = $9698.5 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 = $5950

Rate of Simple Interest (SI) or (R) = 9%

And, Time (t) = 7 years

Thus, Amount (A)

= $5950 + ($5950 × 9% × 7)

= $5950 + ($5950 ×⁹/₁₀₀ × 7)

= $5950 + (^{5950 × 9 × 7}/₁₀₀)

= $5950 + (^{53550 × 7}/₁₀₀)

= $5950 + (³⁷⁴⁸⁵⁰/₁₀₀)

= $5950 + $3748.5 = $9698.5

Thus, Amount (A) to be paid = $9698.5 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 9%

This, means, $9 per $100 per year

∵ For $100, the simple interest for 1 year = $9

∴ For $1, the simple interest for 1 year = ⁹/₁₀₀

∴ For $5950, the simple interest in 1 year

= ⁹/₁₀₀ × 5950

= ^{9 × 5950}/₁₀₀

= ⁵³⁵⁵⁰/₁₀₀ = $535.5

Thus, simple interest for 1 year = $535.5

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $535.5 × 7 = $3748.5

Thus, Simple Interest (SI) = $3748.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5950 + $3748.5

= $9698.5

Thus, Amount to be paid = $9698.5 Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?

(2) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?

(3) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(4) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

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

(6) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 3 years.

(8) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.

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

(10) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.