Mrs. Hart, at age 65, can expect to live for 25 years. If she can invest at 8% per annum compounded monthly, how much does she need now to guarantee herself $300 every month for the next 25 years?
Present Value
= 900(1 - 1.0041666..)^-300)/.0041666...
= $153,954.05
I have calculated this, but it is wrong. Any ideas?
To find out how much Mrs. Hart needs to invest now to guarantee herself $300 every month for the next 25 years, we need to calculate the present value of an annuity.
The formula for the present value of an annuity is:
PV = PMT × (1 - (1 + r/n)^(-nt)) / (r/n),
Where:
PV = Present value of the annuity,
PMT = Payment amount per period,
r = Interest rate per period,
n = Number of compounding periods per year, and
t = Number of years.
In this case, the payment amount (PMT) is $300, the interest rate (r) is 8% (or 0.08), the compounding periods per year (n) is 12 (since it is compounded monthly), and the number of years (t) is 25.
Substituting these values into the formula, we get:
PV = 300 × (1 - (1 + 0.08/12)^(-12×25)) / (0.08/12).
First, we need to calculate the value inside the brackets:
(1 + 0.08/12)^(-12×25) ≈ 0.262663.
Now, we can substitute this value into the formula:
PV = 300 × (1 - 0.262663) / (0.08/12).
Simplifying further:
PV = 300 × (0.737337) / (0.00666667).
PV ≈ $40,193.59.
Therefore, Mrs. Hart needs to invest approximately $40,193.59 now to guarantee herself $300 every month for the next 25 years, assuming an interest rate of 8% per annum compounded monthly.