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) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.

(2) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(3) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(4) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(5) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?

(6) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.

(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?

(9) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.

(10) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?