Simple Interest
Math MCQs

Question :    Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.

Correct Answer  $9810

Solution & Explanation

Solution

Given,

Principal (P) = $5450

Rate of Simple Interest (SI) = 10%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5450 × 10% × 8

= $5450 ×¹⁰/₁₀₀ × 8

= ^{5450 × 10 × 8}/₁₀₀

= ^{54500 × 8}/₁₀₀

= ⁴³⁶⁰⁰⁰/₁₀₀

= $4360

Thus, Simple Interest = $4360

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 = $5450 + $4360

= $9810

Thus, Amount to be paid = $9810 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 = $5450

Rate of Simple Interest (SI) or (R) = 10%

And, Time (t) = 8 years

Thus, Amount (A)

= $5450 + ($5450 × 10% × 8)

= $5450 + ($5450 ×¹⁰/₁₀₀ × 8)

= $5450 + (^{5450 × 10 × 8}/₁₀₀)

= $5450 + (^{54500 × 8}/₁₀₀)

= $5450 + (⁴³⁶⁰⁰⁰/₁₀₀)

= $5450 + $4360 = $9810

Thus, Amount (A) to be paid = $9810 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 10%

This, means, $10 per $100 per year

∵ For $100, the simple interest for 1 year = $10

∴ For $1, the simple interest for 1 year = ¹⁰/₁₀₀

∴ For $5450, the simple interest in 1 year

= ¹⁰/₁₀₀ × 5450

= ^{10 × 5450}/₁₀₀

= ⁵⁴⁵⁰⁰/₁₀₀ = $545

Thus, simple interest for 1 year = $545

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $545 × 8 = $4360

Thus, Simple Interest (SI) = $4360

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5450 + $4360

= $9810

Thus, Amount to be paid = $9810 Answer

Similar Questions

(1) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 6% simple interest?

(2) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(3) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 8 years.

(5) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?

(6) How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?

(7) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(9) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?

(10) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 4% simple interest?