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) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?

(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(4) If David borrowed $3400 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(5) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(6) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?

(7) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.

(8) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.

(10) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.