Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

Correct Answer  $7605

Solution & Explanation

Solution

Given,

Principal (P) = $5850

Rate of Simple Interest (SI) = 3%

Time (t) = 10 years

Thus, Amount (A) = ?

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

Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 10

= $5850 ׳/₁₀₀ × 10

= ^{5850 × 3 × 10}/₁₀₀

= ^{17550 × 10}/₁₀₀

= ¹⁷⁵⁵⁰⁰/₁₀₀

= $1755

Thus, Simple Interest = $1755

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 + $1755

= $7605

Thus, Amount to be paid = $7605 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) = 3%

And, Time (t) = 10 years

Thus, Amount (A)

= $5850 + ($5850 × 3% × 10)

= $5850 + ($5850 ׳/₁₀₀ × 10)

= $5850 + (^{5850 × 3 × 10}/₁₀₀)

= $5850 + (^{17550 × 10}/₁₀₀)

= $5850 + (¹⁷⁵⁵⁰⁰/₁₀₀)

= $5850 + $1755 = $7605

Thus, Amount (A) to be paid = $7605 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 3%

This, means, $3 per $100 per year

∵ For $100, the simple interest for 1 year = $3

∴ For $1, the simple interest for 1 year = ³/₁₀₀

∴ For $5850, the simple interest in 1 year

= ³/₁₀₀ × 5850

= ^{3 × 5850}/₁₀₀

= ¹⁷⁵⁵⁰/₁₀₀ = $175.5

Thus, simple interest for 1 year = $175.5

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $175.5 × 10 = $1755

Thus, Simple Interest (SI) = $1755

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5850 + $1755

= $7605

Thus, Amount to be paid = $7605 Answer

Similar Questions

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

(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.

(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?

(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 3% simple interest?

(5) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?

(7) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

(8) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.

(9) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.

(10) How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?