Simple Interest
Math MCQs

Question :  ( 1 of 10 )  Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

Correct Answer  $7975

Solution & Explanation

Solution

Given,

Principal (P) = $5500

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) = $5500 × 5% × 9

= $5500 ×⁵/₁₀₀ × 9

= ^{5500 × 5 × 9}/₁₀₀

= ^{27500 × 9}/₁₀₀

= ²⁴⁷⁵⁰⁰/₁₀₀

= $2475

Thus, Simple Interest = $2475

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 = $5500 + $2475

= $7975

Thus, Amount to be paid = $7975 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 = $5500

Rate of Simple Interest (SI) or (R) = 5%

And, Time (t) = 9 years

Thus, Amount (A)

= $5500 + ($5500 × 5% × 9)

= $5500 + ($5500 ×⁵/₁₀₀ × 9)

= $5500 + (^{5500 × 5 × 9}/₁₀₀)

= $5500 + (^{27500 × 9}/₁₀₀)

= $5500 + (²⁴⁷⁵⁰⁰/₁₀₀)

= $5500 + $2475 = $7975

Thus, Amount (A) to be paid = $7975 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 $5500, the simple interest in 1 year

= ⁵/₁₀₀ × 5500

= ^{5 × 5500}/₁₀₀

= ²⁷⁵⁰⁰/₁₀₀ = $275

Thus, simple interest for 1 year = $275

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $275 × 9 = $2475

Thus, Simple Interest (SI) = $2475

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5500 + $2475

= $7975

Thus, Amount to be paid = $7975 Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

(3) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?

(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?

(6) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.

(9) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.

(10) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.