Earl Watkins is ready to retired and has saved up $250,000 for that purpose. He places all of this money into an account which will pay him annual payments for 20 years. How large will these annual payments be if the account earns 17% compounded annually?
Wow, 17% interest from a savings account ?
anyway ....
P( 1 - 1.17^-20)/.17 = 250000
..
P = $57, 309.99
this might seem unreasonably high, but remember the interest rate is unreasonable,
As a matter of fact his fund will earn .17(250,000)
or $42,500 in interest the first year, so the fund will only decrease by 57310 - 42500 or $ 14,810
To calculate the size of the annual payments, we need to use the concept of present value (PV) and the formula for the present value of an annuity. The present value of an annuity formula is as follows:
PV = C × [1 - (1 + r)^(-n)] / r
Where:
PV = Present Value (amount of money being invested)
C = Annual payment
r = Interest rate per period (in this case, it's 17% or 0.17)
n = Number of periods (in this case, it's 20 years)
The present value (PV) is provided and equal to $250,000. Plugging this value into the formula, we can solve for C:
$250,000 = C × [1 - (1 + 0.17)^(-20)] / 0.17
Now let's solve for C:
$250,000 × 0.17 = C × [1 - (1 + 0.17)^(-20)]
$42,500 = C × [1 - (1.17)^(-20)]
1 - (1.17)^(-20) ≈ 0.9196
$42,500 = 0.9196C
Divide both sides of the equation by 0.9196:
C ≈ $46,270.71
Therefore, the approximate size of the annual payments that Earl Watkins will receive is $46,270.71.