Simple Interest
Math MCQs

Question :    How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?

Correct Answer  $6150

Solution & Explanation

Solution

Given,

Amount (A) = $6765

Rate of Simple Interest (R) = 2%

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

$6765 = P (1 + 2% × 5)

⇒ $6765 = P (1 + ²/₁₀₀ × 5)

⇒ $6765 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6765 = P (1 + ¹⁰/₁₀₀)

⇒ $6765 = P (^{100 + 10}/₁₀₀)

⇒ $6765 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6765

⇒ P = ⁶⁷⁶⁵/_¹¹⁰/100

⇒ P = 6765 × ¹⁰⁰/₁₁₀

⇒ P = ^{6765 × 100}/₁₁₀

⇒ P = ⁶⁷⁶⁵⁰⁰/₁₁₀

⇒ P = $6150

Thus, the sum borrowed (P) = $6150 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 6765, then the Principal = ¹⁰⁰/₁₁₀ × 6765

= ^{100 × 6765}/₁₁₀

= ⁶⁷⁶⁵⁰⁰/₁₁₀

= 6150

Thus, Principal = $6150

Thus, the sum borrowed = $6150 Answer

Similar Questions

(1) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.

(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 4 years.

(3) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?

(4) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.

(6) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?

(7) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.

(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.

(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.

(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.