Simple Interest
MCQs Math


Question:     How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?


Correct Answer  $7150

Solution And Explanation

Solution

Given,

Amount (A) = $8580

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

$8580 = P (1 + 4% × 5)

⇒ $8580 = P (1 + 4/100 × 5)

⇒ $8580 = P (1 + 4 × 5/100)

⇒ $8580 = P (1 + 20/100)

⇒ $8580 = P (100 + 20/100)

⇒ $8580 = P × 120/100

⇒ P × 120/100 = $8580

⇒ P = 8580/120/100

⇒ P = 8580 × 100/120

⇒ P = 8580 × 100/120

⇒ P = 858000/120

⇒ P = $7150

Thus, the sum borrowed (P) = $7150 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 8580, then the Principal = 100/120 × 8580

= 100 × 8580/120

= 858000/120

= 7150

Thus, Principal = $7150

Thus, the sum borrowed = $7150 Answer


Similar Questions

(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.

(3) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.

(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?

(5) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.

(6) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.

(7) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?

(8) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.

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

(10) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.


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