Simple Interest
Math MCQs

Question :    How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?

Correct Answer  $7050

Solution & Explanation

Solution

Given,

Amount (A) = $8460

Rate of Simple Interest (R) = 4%

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

$8460 = P (1 + 4% × 5)

⇒ $8460 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8460 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8460 = P (1 + ²⁰/₁₀₀)

⇒ $8460 = P (^{100 + 20}/₁₀₀)

⇒ $8460 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8460

⇒ P = ⁸⁴⁶⁰/_¹²⁰/100

⇒ P = 8460 × ¹⁰⁰/₁₂₀

⇒ P = ^{8460 × 100}/₁₂₀

⇒ P = ⁸⁴⁶⁰⁰⁰/₁₂₀

⇒ P = $7050

Thus, the sum borrowed (P) = $7050 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 8460, then the Principal = ¹⁰⁰/₁₂₀ × 8460

= ^{100 × 8460}/₁₂₀

= ⁸⁴⁶⁰⁰⁰/₁₂₀

= 7050

Thus, Principal = $7050

Thus, the sum borrowed = $7050 Answer

Similar Questions

(1) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

(2) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

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

(4) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.

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

(7) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?

(8) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.

(9) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?

(10) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.