Simple Interest
Math MCQs

Question :    Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $4800

Solution & Explanation

Solution

Given,

Amount (A) = $5088

Rate of Simple Interest (R) = 2%

Time (T) = 3 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$5088 = P (1 + 2% × 3)

⇒ $5088 = P (1 + ²/₁₀₀ × 3)

⇒ $5088 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $5088 = P (1 + ⁶/₁₀₀)

⇒ $5088 = P (^{100 + 6}/₁₀₀)

⇒ $5088 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $5088

⇒ P = ⁵⁰⁸⁸/_¹⁰⁶/100

⇒ P = 5088 × ¹⁰⁰/₁₀₆

⇒ P = ^{5088 × 100}/₁₀₆

⇒ P = ⁵⁰⁸⁸⁰⁰/₁₀₆

⇒ P = $4800

Thus, the sum borrowed (P) = $4800 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 5088, then the Principal = ¹⁰⁰/₁₀₆ × 5088

= ^{100 × 5088}/₁₀₆

= ⁵⁰⁸⁸⁰⁰/₁₀₆

= 4800

Thus, Principal = $4800

Thus, the sum borrowed = $4800 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

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

(3) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.

(5) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?

(6) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?

(8) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 3 years.

(10) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.