Simple Interest
Math MCQs

Question :    Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $4050

Solution & Explanation

Solution

Given,

Amount (A) = $4536

Rate of Simple Interest (R) = 4%

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

$4536 = P (1 + 4% × 3)

⇒ $4536 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4536 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4536 = P (1 + ¹²/₁₀₀)

⇒ $4536 = P (^{100 + 12}/₁₀₀)

⇒ $4536 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4536

⇒ P = ⁴⁵³⁶/_¹¹²/100

⇒ P = 4536 × ¹⁰⁰/₁₁₂

⇒ P = ^{4536 × 100}/₁₁₂

⇒ P = ⁴⁵³⁶⁰⁰/₁₁₂

⇒ 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4536, then the Principal = ¹⁰⁰/₁₁₂ × 4536

= ^{100 × 4536}/₁₁₂

= ⁴⁵³⁶⁰⁰/₁₁₂

= 4050

Thus, Principal = $4050

Thus, the sum borrowed = $4050 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.

(2) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.

(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?

(4) How much loan did Kevin borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8520 to clear it?

(5) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.

(8) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 5% simple interest?