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) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?

(2) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?

(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.

(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(5) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?

(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.

(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?

(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 4 years.

(9) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?

(10) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.