Simple Interest
Math MCQs

Question :    Lisa had to pay $4293 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  $4050

Solution & Explanation

Solution

Given,

Amount (A) = $4293

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

$4293 = P (1 + 2% × 3)

⇒ $4293 = P (1 + ²/₁₀₀ × 3)

⇒ $4293 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4293 = P (1 + ⁶/₁₀₀)

⇒ $4293 = P (^{100 + 6}/₁₀₀)

⇒ $4293 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4293

⇒ P = ⁴²⁹³/_¹⁰⁶/100

⇒ P = 4293 × ¹⁰⁰/₁₀₆

⇒ P = ^{4293 × 100}/₁₀₆

⇒ P = ⁴²⁹³⁰⁰/₁₀₆

⇒ P = $4050

Thus, the sum borrowed (P) = $4050 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 4293, then the Principal = ¹⁰⁰/₁₀₆ × 4293

= ^{100 × 4293}/₁₀₆

= ⁴²⁹³⁰⁰/₁₀₆

= 4050

Thus, Principal = $4050

Thus, the sum borrowed = $4050 Answer

Similar Questions

(1) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?

(3) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.

(4) If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 8 years.

(6) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?

(7) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.

(8) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.

(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 2% simple interest?

(10) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?