Simple Interest
Math MCQs

Question :    How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?

Correct Answer  $6300

Solution & Explanation

Solution

Given,

Amount (A) = $6930

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

$6930 = P (1 + 2% × 5)

⇒ $6930 = P (1 + ²/₁₀₀ × 5)

⇒ $6930 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6930 = P (1 + ¹⁰/₁₀₀)

⇒ $6930 = P (^{100 + 10}/₁₀₀)

⇒ $6930 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6930

⇒ P = ⁶⁹³⁰/_¹¹⁰/100

⇒ P = 6930 × ¹⁰⁰/₁₁₀

⇒ P = ^{6930 × 100}/₁₁₀

⇒ P = ⁶⁹³⁰⁰⁰/₁₁₀

⇒ P = $6300

Thus, the sum borrowed (P) = $6300 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 6930, then the Principal = ¹⁰⁰/₁₁₀ × 6930

= ^{100 × 6930}/₁₁₀

= ⁶⁹³⁰⁰⁰/₁₁₀

= 6300

Thus, Principal = $6300

Thus, the sum borrowed = $6300 Answer

Similar Questions

(1) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.

(2) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10168 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.

(4) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?

(5) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?

(6) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.

(7) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(8) Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?