Simple Interest
Math MCQs

Question :    Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.

Correct Answer  $4672

Solution & Explanation

Solution

Given,

Principal (P) = $3650

Rate of Simple Interest (SI) = 7%

Time (t) = 4 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% × 4

= $3650 ×⁷/₁₀₀ × 4

= ^{3650 × 7 × 4}/₁₀₀

= ^{25550 × 4}/₁₀₀

= ¹⁰²²⁰⁰/₁₀₀

= $1022

Thus, Simple Interest = $1022

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 + $1022

= $4672

Thus, Amount to be paid = $4672 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) = 4 years

Thus, Amount (A)

= $3650 + ($3650 × 7% × 4)

= $3650 + ($3650 ×⁷/₁₀₀ × 4)

= $3650 + (^{3650 × 7 × 4}/₁₀₀)

= $3650 + (^{25550 × 4}/₁₀₀)

= $3650 + (¹⁰²²⁰⁰/₁₀₀)

= $3650 + $1022 = $4672

Thus, Amount (A) to be paid = $4672 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 4 years

= Simple interest for 1 year × 4

= $255.5 × 4 = $1022

Thus, Simple Interest (SI) = $1022

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3650 + $1022

= $4672

Thus, Amount to be paid = $4672 Answer

Similar Questions

(1) Linda had to pay $3852.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.

(3) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.

(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?

(5) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?

(7) 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.

(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.

(9) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(10) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.