Question

How do I work this problem out to get these answers? Thanks!

How much money (in dollars) should you invest today at an annual interest rate of 7.3% compounded continuously so that, starting two years from today, you can make annual withdrawals of $4000 in perpetuity? If the annual withdrawals continue indefinitely, how much money should you invest today? First find the largest terms of the infinite series, then find the total amount you should invest today. Enter the three largest terms of the infinite series in order from larger to smaller as numbers (Round your answers to 3 decimal places.) Money Invested = 3456.631 + 3213.287 + 2987.074 Computer's answer now shown above. You are correct. Your receipt no. is 157-1910 Previous Tries Previous Tries: 3673.079 3123.287 3456.631 3673.079 3456.631 3123.287 3456.631 312.287 2987.074 3456.631 3213.287 2987.074 What is the total dollar amount you should invest today? (Round your answer to the nearest cent.) Money Invested - 49100.4500 dollars Computer's answer now shown above

Answer 1

Given,

Interest rate = 7.3%

Amount to be withdrawn after two years indefinetly = $4000.

Present value of amount to be invested at the end of two years :-

PV = $4000/(1+0.073) + $4000/(1+0.073)² + $4000/(1+0.073)³...........

This forms geometric profession.

Sum of geometric progression is a/1-r

a = $4000/(1+0.073)

r = 1/(1+0.073)

There fore present value is

PV = $4000/(1+0.073)/1 - (1/(1+0.073))

On solving this we get

PV = $4000/0.073

PV = $54794.

This is present value at the end of two years.

Present value as on today = $54794/(1+0.073)2

Amount to be invested as on today = $47591.