Question

Q1. A daily perpetuity of $3.33 is to be valued when the effective annual rate of interest is 8.25%. What is the present value of this perpetuity? (Hint: must use the daily periodic rate - use rate to 8th decimal place, when stated in decimal form).

Q2. Our clients saved $2,500,000 for retirement. They wish to withdraw $20,000 from the fund each month for expenses. How long will their retirement savings last if the fund is earning 9% APR compounded monthly?

Enter answer in years, rounded to the nearest first decimal, as in "4.6" years.

Q3. Our clients saved $2,500,000 for retirement. They wish to withdraw $20,000 from the fund each month for expenses. How long will their retirement savings last if the fund is earning 3% APR compounded monthly?

Enter answer in years, rounded to the nearest first decimal, as in "4.6" years.

Answer 1

Answer : 1) Calculation of Present Value of Perpetuity

Present Value of Perpertuity = Daily perpetuity / Interest rate

Interest rate = 8.25% / 365 = 0.022602734% or 0.00226027

Present Value of Perpertuity = Daily perpetuity / Interest rate

= 3.33 / 0.00022603

= 14732.7277459 or $14732.73

Answer : 2 Calculation of Number of Years :

Number of Years can be calculated using NPER function of Excel

=NPER(rate,pmt,pv,fv)

where

rate is the rate of interest per period i.e 9%/12 = 0.75%

pmt is the periodic monthly withdrawals i.e 20000

pv is the present value i.e 2500000

fv will be taken as 0

=NPER(0.75%,20000,-2500000,0)

Therefore number of periods is 371.0630643 months

The number of periods in years = 371.0630643 / 12 = 30.9 years

Answer : 3 Calculation of Number of Years :

Number of Years can be calculated using NPER function of Excel

=NPER(rate,pmt,pv,fv)

where

rate is the rate of interest per period i.e 3%/12 = 0.25%

pmt is the periodic monthly withdrawals i.e 20000

pv is the present value i.e 2500000

fv will be taken as 0

=NPER(0.25%,20000,-2500000,0)

Therefore number of periods is 150.0646485 months

The number of periods in years = 150.0646485 / 12 = 12.5 years