Simple Interest
Math MCQs

Question :    Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.

Correct Answer  $9046.5

Solution & Explanation

Solution

Given,

Principal (P) = $5550

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) = $5550 × 9% × 7

= $5550 ×⁹/₁₀₀ × 7

= ^{5550 × 9 × 7}/₁₀₀

= ^{49950 × 7}/₁₀₀

= ³⁴⁹⁶⁵⁰/₁₀₀

= $3496.5

Thus, Simple Interest = $3496.5

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 = $5550 + $3496.5

= $9046.5

Thus, Amount to be paid = $9046.5 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 = $5550

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

And, Time (t) = 7 years

Thus, Amount (A)

= $5550 + ($5550 × 9% × 7)

= $5550 + ($5550 ×⁹/₁₀₀ × 7)

= $5550 + (^{5550 × 9 × 7}/₁₀₀)

= $5550 + (^{49950 × 7}/₁₀₀)

= $5550 + (³⁴⁹⁶⁵⁰/₁₀₀)

= $5550 + $3496.5 = $9046.5

Thus, Amount (A) to be paid = $9046.5 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 $5550, the simple interest in 1 year

= ⁹/₁₀₀ × 5550

= ^{9 × 5550}/₁₀₀

= ⁴⁹⁹⁵⁰/₁₀₀ = $499.5

Thus, simple interest for 1 year = $499.5

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $499.5 × 7 = $3496.5

Thus, Simple Interest (SI) = $3496.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5550 + $3496.5

= $9046.5

Thus, Amount to be paid = $9046.5 Answer

Similar Questions

(1) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?

(2) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?

(3) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.

(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 6% simple interest?

(5) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.

(6) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?

(7) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?

(9) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(10) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.