Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 74.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns 74.0 when he fully retires, he will wants to have $3,311,865.00 in his retirement account. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be? Assume a 8.00% interest rate
Answer format: Currency: Round to: 2 decimal places.

A firm will pay a dividend of $1.18 next year. The dividend is expected to grow at a constant rate of 4.93% forever and the required rate of return is 14.67%. What is the value of the stock?

Answer format: Currency: Round to: 2 decimal places.

Today is Derek’s 25th birthday. Derek has been advised that he needs to have $2,103,378.00 in his retirement account the day he turns 65. He estimates his retirement account will pay 4.00% interest. Assume he chooses not to deposit anything today. Rather he chooses to make annual deposits into the retirement account starting on his 28.00th birthday and ending on his 65th birthday. How much must those deposits be?

Answer format: Currency: Round to: 2 decimal places.

I would appreciate the help! :)

Answer 1

Part1:

Time period from 26th birthday to 65th birthday: 40 contributions(at beginning of year)

Time period between 65th birthday and 74th birthday: 10 years including 75th birthday pay out

amount required at 75th Birthday: $3,311,865.00

discounting this amount to 65th birthday at 8%: $1,534,034.30, this is the amount of annuity total requirement at 65th birthday for the aforementioned amount to be accumulated by 74th birthday.

Hence calculating annuity for future value at 8% with time period of 30 years (payments) to fetch a future value of $1,534,034.30, is $5482.98(approximately)

FV = A × [(1+I)^n−1​]/I

where: A = Cash deposit amount for each period

I =Interest rate

T=Number of years

We have the FV value and hence doing back calculation to calculate A.

Hence, Derek needs to save $12538.51 from 26th birthday to 64th birthday to reach his goal.

Part 2: Dividend for next year = $1.18, growth rate of dividend = 4.93%, required rate of return is 14.67%

Hence, stock value = (Dividend expected next year)/(required rate of return - growth rate)

= 1.18/(14.67%-4.93%)

= 1.18/9.74% = $12.11 the stock price

Part 3:

Derek requires $2,103,378.00, he will start putting money from his 28th birthday to 65th birthday,

Hence, 38 payments in total at 4% rate.

calculating annuity required for 38 years at 4% to fetch a Total of $2,103,378.00

Using the above formulae:FV = A × [(1+I)^n−1​]/I

amount required for yearly deposit is $23525.31