Simple Interest
Math MCQs

Question :    Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.

Correct Answer  $6798

Solution & Explanation

Solution

Given,

Principal (P) = $5150

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) = $5150 × 4% × 8

= $5150 ×⁴/₁₀₀ × 8

= ^{5150 × 4 × 8}/₁₀₀

= ^{20600 × 8}/₁₀₀

= ¹⁶⁴⁸⁰⁰/₁₀₀

= $1648

Thus, Simple Interest = $1648

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 = $5150 + $1648

= $6798

Thus, Amount to be paid = $6798 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 = $5150

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

And, Time (t) = 8 years

Thus, Amount (A)

= $5150 + ($5150 × 4% × 8)

= $5150 + ($5150 ×⁴/₁₀₀ × 8)

= $5150 + (^{5150 × 4 × 8}/₁₀₀)

= $5150 + (^{20600 × 8}/₁₀₀)

= $5150 + (¹⁶⁴⁸⁰⁰/₁₀₀)

= $5150 + $1648 = $6798

Thus, Amount (A) to be paid = $6798 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 $5150, the simple interest in 1 year

= ⁴/₁₀₀ × 5150

= ^{4 × 5150}/₁₀₀

= ²⁰⁶⁰⁰/₁₀₀ = $206

Thus, simple interest for 1 year = $206

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $206 × 8 = $1648

Thus, Simple Interest (SI) = $1648

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5150 + $1648

= $6798

Thus, Amount to be paid = $6798 Answer

Similar Questions

(1) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.

(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?

(3) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(4) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.

(6) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?

(7) If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.

(9) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 3 years.

(10) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?