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) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 8% simple interest?

(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?

(3) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(4) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?

(5) Joseph took a loan of $5400 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.

(6) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) What amount does William have to pay after 5 years if he takes a loan of $3500 at 9% simple interest?

(8) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 4 years.

(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?

(10) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.