Simple Interest
Math MCQs

Question :    What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?

Correct Answer  $4927.5

Solution & Explanation

Solution

Given,

Principal (P) = $3650

Rate of Simple Interest (SI) = 7%

Time (t) = 5 years

Thus, Amount (A) = ?

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

Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 5

= $3650 ×⁷/₁₀₀ × 5

= ^{3650 × 7 × 5}/₁₀₀

= ^{25550 × 5}/₁₀₀

= ¹²⁷⁷⁵⁰/₁₀₀

= $1277.5

Thus, Simple Interest = $1277.5

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 + $1277.5

= $4927.5

Thus, Amount to be paid = $4927.5 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) = 7%

And, Time (t) = 5 years

Thus, Amount (A)

= $3650 + ($3650 × 7% × 5)

= $3650 + ($3650 ×⁷/₁₀₀ × 5)

= $3650 + (^{3650 × 7 × 5}/₁₀₀)

= $3650 + (^{25550 × 5}/₁₀₀)

= $3650 + (¹²⁷⁷⁵⁰/₁₀₀)

= $3650 + $1277.5 = $4927.5

Thus, Amount (A) to be paid = $4927.5 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 7%

This, means, $7 per $100 per year

∵ For $100, the simple interest for 1 year = $7

∴ For $1, the simple interest for 1 year = ⁷/₁₀₀

∴ For $3650, the simple interest in 1 year

= ⁷/₁₀₀ × 3650

= ^{7 × 3650}/₁₀₀

= ²⁵⁵⁵⁰/₁₀₀ = $255.5

Thus, simple interest for 1 year = $255.5

Therefore, simple interest for 5 years

= Simple interest for 1 year × 5

= $255.5 × 5 = $1277.5

Thus, Simple Interest (SI) = $1277.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3650 + $1277.5

= $4927.5

Thus, Amount to be paid = $4927.5 Answer

Similar Questions

(1) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.

(3) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?

(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.

(5) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(6) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?

(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.

(8) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

(10) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.