Hey,

just starting out with this topic and having a few problems, maybe some of you can help me out.

What quarterly payment is necessary to accumulate $1 million over 10 years if the annual percentage rate (APR) is 8 percent, compounded quarterly? Assume payments are made at the beginning of each quarter.

I'm getting 1.02 as the effective quarterly rate. Is this right? Then all I have to do is calculate payment by using future value of annuity formula right?

I am getting $15,096.35

Not 100% sure tho.

FVoa = PMT [((1 + i)^n - 1) / i]

1,000,000 / (((1.02^40)-1)/.02) = PMT

PMT = 16,555.75

Didn't do the calc but your set up is right.

yeah its 16555.75

$1,000,000 / Future value of an annuity @ 2% for 40 periods (60.402)

pv table here in case you want to try a different rate

Not exactly 1.02 but should be close enough to get a decent number.

The effective quarterly rate would be 1.08^(1/4), so a sliver above 1.0194

the compounding factor is:

1 + 1/[(1+(r/n))^nt]

n = number of times compounding
t = periods in terms of quarters

Noob question, won't $1m in 10 years have about the same purchasing power as $500k today?

Gullanian: Depends on how you compound it and at what interest rate. You are basically saying, assuming annual compounding:

2 = (1+r)^10

ln2 = 10 ln(1+r)

ln2 / 10 = ln (1+r)

.0693 = ln (1+r)

e^.0693 = 1+r

r = 7.1758%

In today's day, good luck finding 7.1758% interest rates.

I don't get what's the difference between n and t, sounds like the same thing. The textbook I use gives me a formula to find the effective rate for any period which is:

k = ( 1 + Quoted Rate/ M )^(m/f) - 1

where m= No. of times interest compounded per quoted period
and f= Number of sub periods in the quoted period

I guess its the same one you mentionned right? Isn't the interest compounded always as many times as the number of sub periods?

yes, it is the same thing. n = compounding in a year. t = years.

Is it simply t = years or years in terms of period?

And say I am given an nominal interest rate of 8% but for 2 years, t would be 2 or .5?

In my formula, you can see I raise it to the (nt) power. Using my definitions, which I think will cause less problems as you do these problems, equals the amount of periods.

If you are given a nominal interest rate of 8% for 2 years, here are three examples:

Annual compounding: (1 + .08/1)^2

Semi-annual: (1 + .08/2)^4

Quarterly: (1 + .08/4)^8

I use T = 2 in each of these examples, but the n changes depending on how many times you compound it.

I wish I used this forum when I took Finance

Most homework problems threads are usually closed I think. Some of this stuff is still fun though.