How much would $200 invested at 4% interest compounded monthly be worth after 30 years?

Question

How much would $200 invested at 4% interest compounded monthly be worth after 30 years?

Answer 1

Use the formula

 

A = P(1 + (r/n))^nt

 

where:

A = amount accumulated

P = investment

r = interest rate (decimal form)

t = time (in years)

n = number of times compounded per year

 

Given:

P = 200

r = 0.04

t = 30

n = 12

 

Note that n=12 because the money is compounded monthly.  There are 12 months in a year.  So the amount is compounded 12 times in a year.

 

Plug in the values into the formula to solve for A.

 

Answer 2

Without using a specific formula:

 

You calculate the percentage first, 4% of 200

 

In this case dollars, $8 per month, if monthly compounded is referred to this.

 

The 4% of interest of $200.00 is equal to $8.

 

How much this interest will be worth after 30 years?

 

30 years are equal to 360 months, for in this term of time, the interest of $8 per month will adds up to $ 2,880.00, given from multiplying 360 per 8, or 12 per 8, the term of a year,  equal to96, and this last one per 30.

Answer 3

Consider the equation

 

T = P * ((1+i/n)^nt)

 

where P is the principal sum, in this case 200, n is the number of times the interest was compounded, and t is time in years relative to the interest rate 'i'. in this case since we are compounding monthly over the span of 30 years, n would be 12*30 = 360. As for i we simply convert the interest rate into a decimal thus 4% = .04 and t would be 30. Plug in this information and our answer is:

 

T = 200 * ((1+.04/360)^(360*30)) ~ 663.98