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) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(3) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?

(4) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.

(5) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.

(7) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.

(8) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.

(9) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?