Simple Interest
Math MCQs

Question :    What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?

Correct Answer  $5475

Solution & Explanation

Solution

Given,

Principal (P) = $3650

Rate of Simple Interest (SI) = 10%

Time (t) = 5 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) = $3650 × 10% × 5

= $3650 ×¹⁰/₁₀₀ × 5

= ^{3650 × 10 × 5}/₁₀₀

= ^{36500 × 5}/₁₀₀

= ¹⁸²⁵⁰⁰/₁₀₀

= $1825

Thus, Simple Interest = $1825

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 = $3650 + $1825

= $5475

Thus, Amount to be paid = $5475 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 = $3650

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

And, Time (t) = 5 years

Thus, Amount (A)

= $3650 + ($3650 × 10% × 5)

= $3650 + ($3650 ×¹⁰/₁₀₀ × 5)

= $3650 + (^{3650 × 10 × 5}/₁₀₀)

= $3650 + (^{36500 × 5}/₁₀₀)

= $3650 + (¹⁸²⁵⁰⁰/₁₀₀)

= $3650 + $1825 = $5475

Thus, Amount (A) to be paid = $5475 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 $3650, the simple interest in 1 year

= ¹⁰/₁₀₀ × 3650

= ^{10 × 3650}/₁₀₀

= ³⁶⁵⁰⁰/₁₀₀ = $365

Thus, simple interest for 1 year = $365

Therefore, simple interest for 5 years

= Simple interest for 1 year × 5

= $365 × 5 = $1825

Thus, Simple Interest (SI) = $1825

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3650 + $1825

= $5475

Thus, Amount to be paid = $5475 Answer

Similar Questions

(1) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?

(2) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?

(3) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(4) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.

(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?

(6) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?

(7) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?

(8) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.

(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.