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Annuity
An engineer retires with $650,000 available for
investment. She invests the money in a portfolio which is
expected to have an average return of 5% per annum.
She wants to have the account pay a monthly income to
her and asks the accountant to assume that the income
must last for 20 years. What income can be withdrawn?
The PV for this problem is negative because,
from the point of view of the engineer, the
money flow is outward from her to the
investment portfolio. The value of the regular
payment, which has been solved for on the
right, is positive as it is being paid from the
portfolio to her. We also assume that the future value FV is to be zero since
the income is only to last for 20 years. On this basis the monthly annuity can
be $4289.71
Loan calculations
You wish to purchase a car by taking out a loan. The
current interest rate is 6.5% and you can afford to make
monthly payments of $300. You want to take out the loan
over a period of 6 years and to still owe $10,000 at the
end of that period (you expect an investment to mature at
that time to pay the final amount). How much can you
borrow?
In this case, from your point of view, the
payments and the FV final residual are
outgoing (negative) since they are made to the
bank. We have pressed to find the PV
and this is the amount that can be borrowed. It
will be positive since it is paid to you. In this
case it is clear that you can afford to borrow $24,624.29.
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