Ralph has been awarded some money in a settlement. He has the option to take a lump sum payment of $425,000 or get paid an annuity of $2,000 per month for the next 25 years. Which is the better deal for Ralph and by how much assuming the growth rate of 5.15% per year?
I answered your last post for this kind of problem. How about giving me your thoughts on how to start with this question ?
It is a straightforward problem.
I think the lump sum is the better deal by $91,772.64.
To determine which option is a better deal for Ralph, we need to calculate the present value of the annuity and compare it to the lump sum amount.
Step 1: Calculate the present value of the annuity.
We can use the formula for the present value of an annuity:
PV = PMT x (1 - (1 + r)^-n) / r
Where PV is the present value, PMT is the payment amount per period, r is the interest rate per period, and n is the total number of periods.
In this case, PMT = $2,000 per month, r = 5.15% per year / 12 months = 0.4292% per month, and n = 25 years x 12 months = 300 months.
PV = $2,000 x (1 - (1 + 0.004292)^-300) / 0.004292
PV ≈ $368,392.40
Step 2: Compare the present value of the annuity to the lump sum amount.
The lump sum amount is $425,000.
The difference between the two options is:
Difference = Lump sum amount - Present value of the annuity
Difference = $425,000 - $368,392.40
Difference ≈ $56,607.60
Therefore, the lump sum payment of $425,000 is a better deal for Ralph by approximately $56,607.60.
To determine the better deal for Ralph, we need to compare the present value of the annuity with the lump sum payment. The present value (PV) is the value of future cash flows in today's dollars, taking into account the time value of money.
1. Lump Sum Payment:
The present value (PV) of a lump sum payment can be calculated using the formula:
PV = FV / (1 + r)^n
Where:
FV = future value (425,000 in this case)
r = interest rate per period (5.15% per year)
n = number of periods (1)
Using the formula:
PV = 425,000 / (1 + 0.0515)^1 ≈ $405,703.55
2. Annuity Payments:
The present value (PV) of an annuity can be calculated using the formula:
PV = A * (1 - (1 + r)^(-n)) / r
Where:
A = annuity payment per period (2,000 per month)
r = interest rate per period (5.15% per year)
n = number of periods (25 years * 12 months per year)
Convert the monthly annuity payment to an annual payment:
Annual Payment = 2,000 * 12 = $24,000
Using the formula:
PV = 24,000 * (1 - (1 + 0.0515)^(-25*12)) / 0.0515 ≈ $324,127.64
Comparing the present values:
PV(lump sum) - PV(annuity) = 405,703.55 - 324,127.64 ≈ $81,575.91
Therefore, taking the lump sum payment of $425,000 would be a better deal for Ralph by approximately $81,575.91.