I will do b), you do the others in the same way.
The problem is that the standard formulas for the amount of an annuity are based on the
fact that the payment period and the interest period coincide. This is not the case here.
Since the payments are made annually, and the compounding is monthly, we have to find the effective annual rate equivalent to a rate of 8% per annum, compounded monthly
Let that annual rate be i
(1+i)^1 = (1 + .08/12)^12 = 1.08299507
i = .08299507 (I stored that in my calculator)
b) amount = 1500(1.08299507^20 - 1)/.08299507 = $89,039,13
Do a) and c) in the same way, the i stays the same
d) 1500(1.08299507^n - 1)/.08299507 = 1,000,000
(1.08299507^n - 1)/.08299507 = 666.6666...
(1.08299507^n - 1) = 55.33300454
1.08299507^n = 56.33300454
n log 1.08299507 = log 56.33300454
I get n = 50.559 years
State your appropriate answer.
checking my answer:
amount = 1500(1.08299507^50.559 - 1)/.08299507 = 1,000,016.935 (not bad, using my 3 decimal answer for the years
How much will you have accumulated, if you annually invest $1,500 into an IRA at 8% interest
compounded monthly for:
a. 5 year
b. 20 years
c. 40 years
d. How long will it take to earn your first million dollars? Your answer should be exact
rounded within 2 decimal places. Please use logarithms to solve
1 answer