Simple Interest
Math MCQs

Question :    How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?

Correct Answer  $6400

Solution & Explanation

Solution

Given,

Amount (A) = $7040

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

$7040 = P (1 + 2% × 5)

⇒ $7040 = P (1 + ²/₁₀₀ × 5)

⇒ $7040 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7040 = P (1 + ¹⁰/₁₀₀)

⇒ $7040 = P (^{100 + 10}/₁₀₀)

⇒ $7040 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7040

⇒ P = ⁷⁰⁴⁰/_¹¹⁰/100

⇒ P = 7040 × ¹⁰⁰/₁₁₀

⇒ P = ^{7040 × 100}/₁₁₀

⇒ P = ⁷⁰⁴⁰⁰⁰/₁₁₀

⇒ P = $6400

Thus, the sum borrowed (P) = $6400 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 7040, then the Principal = ¹⁰⁰/₁₁₀ × 7040

= ^{100 × 7040}/₁₁₀

= ⁷⁰⁴⁰⁰⁰/₁₁₀

= 6400

Thus, Principal = $6400

Thus, the sum borrowed = $6400 Answer

Similar Questions

(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?

(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.

(4) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?

(5) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.

(6) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?

(7) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.

(8) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(10) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.