Simple Interest
Math MCQs

Question :    How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?

Correct Answer  $5050

Solution & Explanation

Solution

Given,

Amount (A) = $6060

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

$6060 = P (1 + 4% × 5)

⇒ $6060 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6060 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6060 = P (1 + ²⁰/₁₀₀)

⇒ $6060 = P (^{100 + 20}/₁₀₀)

⇒ $6060 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6060

⇒ P = ⁶⁰⁶⁰/_¹²⁰/100

⇒ P = 6060 × ¹⁰⁰/₁₂₀

⇒ P = ^{6060 × 100}/₁₂₀

⇒ P = ⁶⁰⁶⁰⁰⁰/₁₂₀

⇒ P = $5050

Thus, the sum borrowed (P) = $5050 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 6060, then the Principal = ¹⁰⁰/₁₂₀ × 6060

= ^{100 × 6060}/₁₂₀

= ⁶⁰⁶⁰⁰⁰/₁₂₀

= 5050

Thus, Principal = $5050

Thus, the sum borrowed = $5050 Answer

Similar Questions

(1) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.

(3) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.

(5) How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?

(6) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.

(7) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?

(9) If Jennifer paid $3640 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 Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?