1. If the first deposit is at 36 years and the last expected deposit is at 65 years, then annual deposits will be made for 30 years. Expected annual withdrawals are $90,000 for 15 years from the retirement fund with a bank that offers compound interest of 8% annually. Calculation

Present value (PV) =?

Future value (FV) = (90,000*15) = $1,350,000

Periodic payment amount (PMT) =?

Interest rate per period (Rate) = 8% or 0.08

Number of payment periods (Nper) = 30

Using the Excel function “PV”, the following data is entered into the presented fields Rate = 8%

Nper = 30

PMT =?

Fv = 1,350,000

Type = blank

PMT = $9,416.15

$9,416.15 is the amount required for 30 annual deposits with an 8% compound interest to yield $90,000 for 15 years.

2. If a lump sum amount is deposited on my 35th birthday, then the principle will be compounded for 31 years. Calculation

Using the compound interest formula

A = P (1+r/n) nt

Where; A = final amount, P = principal, r = interest rate n = number of times the interest is compounded per year and t = number of years

P= A/ (1+r/n) ntP = 1,350,000/ (1+0.08/1)31

P =1,350,000/ (1.08)31

P =1,350,000/ 10.868

The amount required for a lump sum deposit is $124,217.89

3.If an additional $1,500 from my employer bonus plan is deposited annually to the retirement account and a $25,000 is added to the account after 19 years (on my 55th birthday), then; using the total annual contribution obtained in (1), The first deductions from my annual contribution will be $1,500 from the bonus plan 4,471.98 – 1,500 = 2,971.98

Distributing the $25,000 over the 30 year period, (25,000/30) = 833.33 2,971.98 – 833.33 = 2,138.65

To make $90,000 withdrawals for 15 years, I will need to make annual deposits of $2,138.65 QUESTION 2:

1.

a) Net Present Value

Using the MS-Excel function of NPV the rate of return (12%) is keyed into the “Rate” field and the returns per period are keyed into the corresponding “Value” field to obtain the present value. For example returns of year 1 will be keyed into the “Value 1” field, returns of year 6 in the “Value 6” field as shown in the tables below. The NPV is obtained by subtracting the initial investment from the sum of the present values.

Option 1:

|Year |Returns |Present value | |1 |50,000 |$44,642.86 | |2 |50,000 |$39,859.69 | |3 |50,000 |$35,589.01 | |4 |50,000 |$31,775.90 | |5 |50,000 |$28,371.34 | |6 |50,000 |$25,331.56 | |7 |50,000 |$22,617.46 | |8 |50,000 |$20,194.16 | |9 |50,000 |$18,030.50 | |10 |550,000 |$177,085.28 | |Sum Of Present Values |$443,497.77 |

NPV for option 1 is (443,497.77-500,000) = -$56,502.23

Option 2:

|Year |Returns |Present value | |1 |60,000 |$53,571.43 | |2 |60,000 |$47,831.63 | |3 |60,000 |$42,706.81 | |4 |60,000 |$38,131.08 | |5 |60,000 |$34,045.61 | |6 |60,000 |$30,397.87 | |7 |60,000 |$27,140.95 | |8 |60,000 |$24,232.99 | |9 |60,000 |$21,636.60 | |10 |810,000 |$260,798.32 | |Sum Of Present Values...