calculus homework

Question

When your first child is born, you begin to save for college by depositing $475 per month in an account paying 12% interest per year. You increase the amount you save by 2% per year. With continuous investment and compounding, how much will have accumulated in the account by the time your child enters college 18 years later? (Round your answer to the nearest cent.)

Answer 1

Hi Dustin, 

 

Let us start with the payment after the first month which is $475

After the first year (12 months), you should have 12*$475 saved.  

Each year you pay 12% interest on the current value you have in the account so you lose 12% of 12*$475 after the first year. 

 

(100%*12*$475) - (12%*12*$475)  = 88%*12*$475 is how much you will have after the first year. 

 

However, each year we save 2% more so we will add 2% to that 88% = 90%

 

After the 2nd year, you should have added another 475*12

88%*12*$475 + 100%*12*$475 = 188%*12*$475

 

but now we have to reduce it by 12% and add 2% = 10%

 

you can see a trend such that 

12*475(1+0.1)¹⁸ gives your how much you have accumulated over the 18 years.

 

In general the formula for this problem is 

P = P₀ (1+r)ⁿ

where

P₀ is the initial investment for the year

r is the yearly rate of increase/decrease

n is the number of years.

 

I hope this clears things up. Let me know if you have any questions. Is this calculus? It doesn't seem like it.