Simple Interest
Math MCQs

Question :    How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?

Correct Answer  $5550

Solution & Explanation

Solution

Given,

Amount (A) = $6105

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

$6105 = P (1 + 2% × 5)

⇒ $6105 = P (1 + ²/₁₀₀ × 5)

⇒ $6105 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6105 = P (1 + ¹⁰/₁₀₀)

⇒ $6105 = P (^{100 + 10}/₁₀₀)

⇒ $6105 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6105

⇒ P = ⁶¹⁰⁵/_¹¹⁰/100

⇒ P = 6105 × ¹⁰⁰/₁₁₀

⇒ P = ^{6105 × 100}/₁₁₀

⇒ P = ⁶¹⁰⁵⁰⁰/₁₁₀

⇒ P = $5550

Thus, the sum borrowed (P) = $5550 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 6105, then the Principal = ¹⁰⁰/₁₁₀ × 6105

= ^{100 × 6105}/₁₁₀

= ⁶¹⁰⁵⁰⁰/₁₁₀

= 5550

Thus, Principal = $5550

Thus, the sum borrowed = $5550 Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?

(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.

(3) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.

(4) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?

(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.

(6) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.

(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.

(9) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

(10) How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?