Simple Interest
Math MCQs

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

Correct Answer  $10450

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (SI) = 9%

Time (t) = 10 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) = $5500 × 9% × 10

= $5500 ×⁹/₁₀₀ × 10

= ^{5500 × 9 × 10}/₁₀₀

= ^{49500 × 10}/₁₀₀

= ⁴⁹⁵⁰⁰⁰/₁₀₀

= $4950

Thus, Simple Interest = $4950

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 + $4950

= $10450

Thus, Amount to be paid = $10450 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) = 9%

And, Time (t) = 10 years

Thus, Amount (A)

= $5500 + ($5500 × 9% × 10)

= $5500 + ($5500 ×⁹/₁₀₀ × 10)

= $5500 + (^{5500 × 9 × 10}/₁₀₀)

= $5500 + (^{49500 × 10}/₁₀₀)

= $5500 + (⁴⁹⁵⁰⁰⁰/₁₀₀)

= $5500 + $4950 = $10450

Thus, Amount (A) to be paid = $10450 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 $5500, the simple interest in 1 year

= ⁹/₁₀₀ × 5500

= ^{9 × 5500}/₁₀₀

= ⁴⁹⁵⁰⁰/₁₀₀ = $495

Thus, simple interest for 1 year = $495

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $495 × 10 = $4950

Thus, Simple Interest (SI) = $4950

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5500 + $4950

= $10450

Thus, Amount to be paid = $10450 Answer

Similar Questions

(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 7 years.

(2) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 5% simple interest?

(3) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.

(5) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.

(7) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?

(8) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?

(9) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.