Simple Interest
Math MCQs

Question :    How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?

Correct Answer  $5050

Solution & Explanation

Solution

Given,

Amount (A) = $5555

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

$5555 = P (1 + 2% × 5)

⇒ $5555 = P (1 + ²/₁₀₀ × 5)

⇒ $5555 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5555 = P (1 + ¹⁰/₁₀₀)

⇒ $5555 = P (^{100 + 10}/₁₀₀)

⇒ $5555 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5555

⇒ P = ⁵⁵⁵⁵/_¹¹⁰/100

⇒ P = 5555 × ¹⁰⁰/₁₁₀

⇒ P = ^{5555 × 100}/₁₁₀

⇒ P = ⁵⁵⁵⁵⁰⁰/₁₁₀

⇒ 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 = 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 5555, then the Principal = ¹⁰⁰/₁₁₀ × 5555

= ^{100 × 5555}/₁₁₀

= ⁵⁵⁵⁵⁰⁰/₁₁₀

= 5050

Thus, Principal = $5050

Thus, the sum borrowed = $5050 Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

(2) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?

(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?

(5) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?

(6) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?

(7) How much loan did Betty borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7187.5 to clear it?

(8) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 3 years.