Simple Interest
Math MCQs

Question :    How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?

Correct Answer  $7400

Solution & Explanation

Solution

Given,

Amount (A) = $8140

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

$8140 = P (1 + 2% × 5)

⇒ $8140 = P (1 + ²/₁₀₀ × 5)

⇒ $8140 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8140 = P (1 + ¹⁰/₁₀₀)

⇒ $8140 = P (^{100 + 10}/₁₀₀)

⇒ $8140 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8140

⇒ P = ⁸¹⁴⁰/_¹¹⁰/100

⇒ P = 8140 × ¹⁰⁰/₁₁₀

⇒ P = ^{8140 × 100}/₁₁₀

⇒ P = ⁸¹⁴⁰⁰⁰/₁₁₀

⇒ P = $7400

Thus, the sum borrowed (P) = $7400 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 8140, then the Principal = ¹⁰⁰/₁₁₀ × 8140

= ^{100 × 8140}/₁₁₀

= ⁸¹⁴⁰⁰⁰/₁₁₀

= 7400

Thus, Principal = $7400

Thus, the sum borrowed = $7400 Answer

Similar Questions

(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.

(2) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?

(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 8 years.

(4) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?

(6) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?

(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.

(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 8 years.

(9) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 3 years.