Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.

Correct Answer  $10769.5

Solution & Explanation

Solution

Given,

Principal (P) = $5950

Rate of Simple Interest (SI) = 9%

Time (t) = 9 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% × 9

= $5950 ×⁹/₁₀₀ × 9

= ^{5950 × 9 × 9}/₁₀₀

= ^{53550 × 9}/₁₀₀

= ⁴⁸¹⁹⁵⁰/₁₀₀

= $4819.5

Thus, Simple Interest = $4819.5

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 + $4819.5

= $10769.5

Thus, Amount to be paid = $10769.5 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) = 9 years

Thus, Amount (A)

= $5950 + ($5950 × 9% × 9)

= $5950 + ($5950 ×⁹/₁₀₀ × 9)

= $5950 + (^{5950 × 9 × 9}/₁₀₀)

= $5950 + (^{53550 × 9}/₁₀₀)

= $5950 + (⁴⁸¹⁹⁵⁰/₁₀₀)

= $5950 + $4819.5 = $10769.5

Thus, Amount (A) to be paid = $10769.5 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 9 years

= Simple interest for 1 year × 9

= $535.5 × 9 = $4819.5

Thus, Simple Interest (SI) = $4819.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5950 + $4819.5

= $10769.5

Thus, Amount to be paid = $10769.5 Answer

Similar Questions

(1) If Sandra paid $4806 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.

(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?

(4) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.

(7) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?

(9) How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.