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) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?

(2) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.

(3) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?

(4) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.

(6) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.

(8) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

(9) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.

(10) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?