Simple Interest
Math MCQs

Question :    What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?

Correct Answer  $4960

Solution & Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (SI) = 10%

Time (t) = 6 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) = $3100 × 10% × 6

= $3100 ×¹⁰/₁₀₀ × 6

= ^{3100 × 10 × 6}/₁₀₀

= ^{31000 × 6}/₁₀₀

= ¹⁸⁶⁰⁰⁰/₁₀₀

= $1860

Thus, Simple Interest = $1860

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 = $3100 + $1860

= $4960

Thus, Amount to be paid = $4960 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 = $3100

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

And, Time (t) = 6 years

Thus, Amount (A)

= $3100 + ($3100 × 10% × 6)

= $3100 + ($3100 ×¹⁰/₁₀₀ × 6)

= $3100 + (^{3100 × 10 × 6}/₁₀₀)

= $3100 + (^{31000 × 6}/₁₀₀)

= $3100 + (¹⁸⁶⁰⁰⁰/₁₀₀)

= $3100 + $1860 = $4960

Thus, Amount (A) to be paid = $4960 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 $3100, the simple interest in 1 year

= ¹⁰/₁₀₀ × 3100

= ^{10 × 3100}/₁₀₀

= ³¹⁰⁰⁰/₁₀₀ = $310

Thus, simple interest for 1 year = $310

Therefore, simple interest for 6 years

= Simple interest for 1 year × 6

= $310 × 6 = $1860

Thus, Simple Interest (SI) = $1860

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3100 + $1860

= $4960

Thus, Amount to be paid = $4960 Answer

Similar Questions

(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.

(2) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.

(3) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(5) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(6) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?

(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 after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.

(9) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.