Simple Interest
Math MCQs

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

Correct Answer  $6050

Solution & Explanation

Solution

Given,

Amount (A) = $7260

Rate of Simple Interest (R) = 4%

Time (T) = 5 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

$7260 = P (1 + 4% × 5)

⇒ $7260 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7260 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7260 = P (1 + ²⁰/₁₀₀)

⇒ $7260 = P (^{100 + 20}/₁₀₀)

⇒ $7260 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7260

⇒ P = ⁷²⁶⁰/_¹²⁰/100

⇒ P = 7260 × ¹⁰⁰/₁₂₀

⇒ P = ^{7260 × 100}/₁₂₀

⇒ P = ⁷²⁶⁰⁰⁰/₁₂₀

⇒ P = $6050

Thus, the sum borrowed (P) = $6050 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 7260, then the Principal = ¹⁰⁰/₁₂₀ × 7260

= ^{100 × 7260}/₁₂₀

= ⁷²⁶⁰⁰⁰/₁₂₀

= 6050

Thus, Principal = $6050

Thus, the sum borrowed = $6050 Answer

Similar Questions

(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.

(2) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.

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

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.

(5) If Jessica borrowed $3750 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(6) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.

(7) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.

(9) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.

(10) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.