Tough calculus problem?

Question

Suppose you contribute $70 per month into a fund that earns 6.15% annual interest. What is the value of your investment after 22 years?

Yeah, I realize it isn't really that tough but I have gotten about 4 hours of sleep in the past two days so I can't think to save my life. All help is appreciated!

Answer 1

Using the formula,
A = (p/i)[(1 + i)^n - 1]
Assuming monthly compounding,
A = (70/0.005125)[(1.005125)^264 - 1]
A = $39,004.27
Assuming annual compounding,
A = (840/0.0615)[(1.0615)^22 - 1]
A = $37,115.79

Answer 2

This is a simple compunding mathematics question. It is not really even Calculus, rather Advanced Algebra.

There is an easy way of doing this:

Year 1 12 months x $70 = 840, but you can not just simply multiply 6.15% because each month is calculated at a pro-rated 1/12 of the 6.15% Annual Yield.
Month 1 = $70.00 x (.1065/12) = .62125 + 70.00 = 70.62125
Month 2 = $70.6125 + $70.00 = $140.6125 x (.10625/12) = 1.2450 + 140.6125 = $141.8575
Month3 = $141.8575 + $70.00 =$211.8575 x (.10625/12) = $1.8802 + $211.8575 = $213.7377
..and so on for each month for 22 years. (there is 264 months)

There is also an equation for compounding interest as long as the 6.15% annual interest yield never changes and the $70.00 per month contribution does not vary either. Look it up in your textbook or do a google search.

Good Luck !!!

Answer 3

Most people would just use a spreadsheet to do that. Which is what I did. This uses OpenOffice.Org to do the calculation $70 per month is $840 a year. 6.15% interest on that is 51.66. Total is 891.66. This is the first year. Second year, we have another 840, plus the 891.66, then 6.15 interest on that.

Cell A1= 70. Cell B1= A1*12. Cell C1=B1 Cell D1=B1*(6.15%) Cell E1=B1+D1

Cell A2=70, Cell B2 = A2*12 Cell C2 =B2+E1 Cell D2=C2*(6.15%) Cell E2=C2+D2.

Copy this row down for 21 years, and in Cell E22, I get 39398.41

The only question is whether I have the interest right; if it's simple interest it should be correct.

Cedric's answer misses the effect of compounding of interest.

Answer 4

Use the annuity formula

F= P(1+i) { (1+i)^n -1} / i
F= 70 (1 + 0.0615/12) { ( 1+0.0615/12)^264-1} / ( 0.0615/12)
F = $39204.17

assuming monthly compounding.

If interest compounded annually but payments monthly
F= $38340.93

Answer 5

f'(x) = -(5x^2+16x)/(5x-8)^4 At x = 5, f(x) = 25/(17^3) and f'(x) = -205/(17^4) The equation of the tangent is: y - y(0) = (-205/(17^4))(x - x(0)), the place (x(0), y(0)) is the element (5, 25/(17^3)) it extremely is switched over to y = (-205/(17^4)) x + 1450/(17^4). you could artwork out the small print of changing the equation into this very final type, and actual you will desire to verify all the above. If i've got made a mistake, a minimum of you have a technique to persist with to maximum appropriate that blunders and arrive at a answer. solid luck.

Answer 6

Assuming that the bank compounds monthly and most funds do.

$39,004.27

You will have made 264 payments and earned $20,524.27
interest

By the way. That's not calculus it's economics.

Answer 7

70*12*(1+0.0615)^22
=$3122.62

Answer 8

i suck at math