Could someone check my math in this annuity problem?

[littlebu]

The problem: When your son is born you deposit $10,000 in an account paying 8% interest compounded quarterly. When he starts college, 18 years later, you plan to withdraw all the money, in monthly installments, over 4 years. How large will each payment be?(the annual rate remains 8%).

First I found what the deposit was worth 18 years later

P=10,000
r=.08
m=4
i=.08/4
n= (18)(4)=72

so

A=10,000(1+.08/4)^72

A=$41,611.40

Now since the problem says the annual rate is 8% I found how much to expect each year and divided by 12.

R= (41,611.40)(.08)/1-(1.08)^-4

R= 12,563.35/yr

so per month is

12,563.35/12 = 1046.95/month

Is this correct?

 

[Denis]

Your 41,611.40 is keerect!
But the rest is wrong

The annual equivalent of 2% quarterly is 1.02^4 - 1
You need a monthly rate i that equals above; so:
(1 + i)^12 = 1.02^4
1 + i = (1.02^4)^(1/12) : remember that (x^a)^b = x^(ab); so:
i = 1.02^(1/3) - 1
i = 1.00662... - 1 = .00662...

So monthly payment is:
41611.40(.00662) / (1 - 1.00662^-48) = 1014.76

OK?

With these, ALWAYS convert the interest rate so that it matches the frequency of payments.

 

[littlebu]

Thank you that makes sense. I was a little confused because of the end where it says "the annual rate remains 8%". Since it didn't specify that it was still quarterly I didn't figure that into the computation. Thank you for your help and for taking the time to check my work.