Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.

Correct Answer  $8231.5

Solution & Explanation

Solution

Given,

Principal (P) = $5050

Rate of Simple Interest (SI) = 7%

Time (t) = 9 years

Thus, Amount (A) = ?

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

Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $5050 × 7% × 9

= $5050 ×⁷/₁₀₀ × 9

= ^{5050 × 7 × 9}/₁₀₀

= ^{35350 × 9}/₁₀₀

= ³¹⁸¹⁵⁰/₁₀₀

= $3181.5

Thus, Simple Interest = $3181.5

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 = $5050 + $3181.5

= $8231.5

Thus, Amount to be paid = $8231.5 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 = $5050

Rate of Simple Interest (SI) or (R) = 7%

And, Time (t) = 9 years

Thus, Amount (A)

= $5050 + ($5050 × 7% × 9)

= $5050 + ($5050 ×⁷/₁₀₀ × 9)

= $5050 + (^{5050 × 7 × 9}/₁₀₀)

= $5050 + (^{35350 × 9}/₁₀₀)

= $5050 + (³¹⁸¹⁵⁰/₁₀₀)

= $5050 + $3181.5 = $8231.5

Thus, Amount (A) to be paid = $8231.5 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 7%

This, means, $7 per $100 per year

∵ For $100, the simple interest for 1 year = $7

∴ For $1, the simple interest for 1 year = ⁷/₁₀₀

∴ For $5050, the simple interest in 1 year

= ⁷/₁₀₀ × 5050

= ^{7 × 5050}/₁₀₀

= ³⁵³⁵⁰/₁₀₀ = $353.5

Thus, simple interest for 1 year = $353.5

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $353.5 × 9 = $3181.5

Thus, Simple Interest (SI) = $3181.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5050 + $3181.5

= $8231.5

Thus, Amount to be paid = $8231.5 Answer

Similar Questions

(1) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(2) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.

(4) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.

(6) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.

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

(9) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.

(10) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.