: Bill Smith, age 25, begins to make yearly deposits of $1600 into his IRS account that pays interest at a quarterly rate of 8% compounded..?
BillSmith, age 25, begins to make yearly deposits of $1600 into his IRS account that pays interest at a quarterly rate of 8% compounded continuously. How much will he have in her bank account if he retires at age 70?
^^How do you use the annuity formula for this? A0= M; An= (1+r/N)An-1 + P
where A0= initial amount
N= # times a year
Please explain step by step if possible. Thank you! TEN POINTS FOR A CORRECT ANSWER :)
- Anonymous6 years agoFavorite Answer
Pf = Pi*(1 + r/n)^(nt)
t = 45, n = 4, plug in the rest
Pi + Pi*r = Pi*(1 + r) .....principal with interest once
Pi + Pi*r + r(Pi + Pi*r) = Pi + Pi*r + Pi*r + Pi*r^2 = Pi(1 + r)^2....principal with interest twice
When interest is compounded the problem becomes complicated. The IRS account is compounded with a quarterly interest, that is a quarter of the interest is paid separately but within an entire year.
Pi + Pi*r/n = Pi(1 + r/n)....compounded interest first time
Pi + Pi*r/n + r/n*(Pi + Pi*r/n) = Pi(1 + r/n)^2...compounded interest second time
We have a pattern here, that is we've noticed that Pf = Pi(1 + r/n)^n but if we replace (1 + r/n)^n to b and ask ourselves how the money will grow when at the end of time t, this becomes Pf = Pi*b^t or Pi*(1 + r/n)^nt
- 6 years ago
Amount at age 70 = $1600* e^ (0.08*(70-25)