Simple Interest
Math MCQs

Question :    What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?

Correct Answer  $3355

Solution & Explanation

Solution

Given,

Principal (P) = $3050

Rate of Simple Interest (SI) = 5%

Time (t) = 2 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) = $3050 × 5% × 2

= $3050 ×⁵/₁₀₀ × 2

= ^{3050 × 5 × 2}/₁₀₀

= ^{15250 × 2}/₁₀₀

= ³⁰⁵⁰⁰/₁₀₀

= $305

Thus, Simple Interest = $305

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 = $3050 + $305

= $3355

Thus, Amount to be paid = $3355 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 = $3050

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

And, Time (t) = 2 years

Thus, Amount (A)

= $3050 + ($3050 × 5% × 2)

= $3050 + ($3050 ×⁵/₁₀₀ × 2)

= $3050 + (^{3050 × 5 × 2}/₁₀₀)

= $3050 + (^{15250 × 2}/₁₀₀)

= $3050 + (³⁰⁵⁰⁰/₁₀₀)

= $3050 + $305 = $3355

Thus, Amount (A) to be paid = $3355 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 $3050, the simple interest in 1 year

= ⁵/₁₀₀ × 3050

= ^{5 × 3050}/₁₀₀

= ¹⁵²⁵⁰/₁₀₀ = $152.5

Thus, simple interest for 1 year = $152.5

Therefore, simple interest for 2 years

= Simple interest for 1 year × 2

= $152.5 × 2 = $305

Thus, Simple Interest (SI) = $305

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3050 + $305

= $3355

Thus, Amount to be paid = $3355 Answer

Similar Questions

(1) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?

(2) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.

(3) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?

(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?

(5) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.

(6) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.

(9) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?

(10) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?