Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.

Correct Answer  $8047.5

Solution & Explanation

Solution

Given,

Principal (P) = $5550

Rate of Simple Interest (SI) = 5%

Time (t) = 9 years

Thus, Amount (A) = ?

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

Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 9

= $5550 ×⁵/₁₀₀ × 9

= ^{5550 × 5 × 9}/₁₀₀

= ^{27750 × 9}/₁₀₀

= ²⁴⁹⁷⁵⁰/₁₀₀

= $2497.5

Thus, Simple Interest = $2497.5

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 + $2497.5

= $8047.5

Thus, Amount to be paid = $8047.5 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) = 5%

And, Time (t) = 9 years

Thus, Amount (A)

= $5550 + ($5550 × 5% × 9)

= $5550 + ($5550 ×⁵/₁₀₀ × 9)

= $5550 + (^{5550 × 5 × 9}/₁₀₀)

= $5550 + (^{27750 × 9}/₁₀₀)

= $5550 + (²⁴⁹⁷⁵⁰/₁₀₀)

= $5550 + $2497.5 = $8047.5

Thus, Amount (A) to be paid = $8047.5 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 5%

This, means, $5 per $100 per year

∵ For $100, the simple interest for 1 year = $5

∴ For $1, the simple interest for 1 year = ⁵/₁₀₀

∴ For $5550, the simple interest in 1 year

= ⁵/₁₀₀ × 5550

= ^{5 × 5550}/₁₀₀

= ²⁷⁷⁵⁰/₁₀₀ = $277.5

Thus, simple interest for 1 year = $277.5

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $277.5 × 9 = $2497.5

Thus, Simple Interest (SI) = $2497.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5550 + $2497.5

= $8047.5

Thus, Amount to be paid = $8047.5 Answer

Similar Questions

(1) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.

(3) How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?

(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.

(5) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?

(6) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(7) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.

(9) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.