Simple Interest
Math MCQs

Question :    Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.

Correct Answer  $7722

Solution & Explanation

Solution

Given,

Principal (P) = $5850

Rate of Simple Interest (SI) = 4%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5850 × 4% × 8

= $5850 ×⁴/₁₀₀ × 8

= ^{5850 × 4 × 8}/₁₀₀

= ^{23400 × 8}/₁₀₀

= ¹⁸⁷²⁰⁰/₁₀₀

= $1872

Thus, Simple Interest = $1872

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 = $5850 + $1872

= $7722

Thus, Amount to be paid = $7722 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 = $5850

Rate of Simple Interest (SI) or (R) = 4%

And, Time (t) = 8 years

Thus, Amount (A)

= $5850 + ($5850 × 4% × 8)

= $5850 + ($5850 ×⁴/₁₀₀ × 8)

= $5850 + (^{5850 × 4 × 8}/₁₀₀)

= $5850 + (^{23400 × 8}/₁₀₀)

= $5850 + (¹⁸⁷²⁰⁰/₁₀₀)

= $5850 + $1872 = $7722

Thus, Amount (A) to be paid = $7722 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 4%

This, means, $4 per $100 per year

∵ For $100, the simple interest for 1 year = $4

∴ For $1, the simple interest for 1 year = ⁴/₁₀₀

∴ For $5850, the simple interest in 1 year

= ⁴/₁₀₀ × 5850

= ^{4 × 5850}/₁₀₀

= ²³⁴⁰⁰/₁₀₀ = $234

Thus, simple interest for 1 year = $234

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $234 × 8 = $1872

Thus, Simple Interest (SI) = $1872

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5850 + $1872

= $7722

Thus, Amount to be paid = $7722 Answer

Similar Questions

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

(2) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?

(3) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

(4) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?

(7) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.

(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 10% simple interest?

(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.

(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 8 years.