Upon retirement (40 years from now) you want to receive "4,000" (amount of money you choose in Part a) each month for a period of 28 years. This money resides in an account that pays 5.8% interest. How much money must be in the account to fulfill your goal?
In order to use our standard compound interest formulas, the payment period must be the same as the compounding period of the interest rate, so I will assume you meant 5.8% per annum compounded monthly.
i = .058/12 = .00483333...
present value of what is needed now .... P
Pick 40 years from now as the focal date
P(1.00483333...)^480 = 4000(1 - 1.00483333..^-336)/.00483333...
(I stored .0048333.. in my calculator's memory, thus keeping the best accuracy possible )
P(10.11896447) = 663,822.3742
P = $65,601.81
To calculate the amount of money that must be in the account to fulfill your goal, we can use the concept of future value of an annuity.
The future value of an annuity formula is:
FV = PMT * [(1 + r)^n - 1] / r
Where:
FV = future value of the annuity (amount of money in the account)
PMT = payment per period (monthly payment of $4,000)
r = interest rate per period (annual interest rate of 5.8% divided by 12 months)
n = number of periods (28 years multiplied by 12 months per year)
Let's plug in the values into the formula and calculate the future value of the annuity:
PMT = $4,000
r = 5.8% / 12 = 0.0483333 (approx.)
n = 28 * 12 = 336
FV = $4,000 * [(1 + 0.0483333)^336 - 1] / 0.0483333
Now let's solve for FV using a calculator or spreadsheet software.
The future value of the annuity will tell us how much money must be in the account to fulfill your goal of receiving $4,000 each month for 28 years with a 5.8% interest rate.