PV and FV

[K_Swiss]

Please check my answers if they are correct or not.

At the end of each of the next 23 years, an individual makes a fixed annual deposit into a retirement savings account that has an annual interest rate of 7.5%. If the account has a balance of $50,000 at the end of 23 years, how much did the individual deposit each year?

Answer: 877

Work:
50 000 = CF [(1 + 0.075)^23 - 1]/0.075
CF = 877

You have just won the lottery. You will receive $32,000 for 20 years with payments made at the end of each year. Given a 5% discount rate, what is the present value of this payment stream?

Answer: 398,791

Work:
Vo = 32 000 [1 - 1/(1 + 0.05)^20]/.05 = 398 791

If you deposit $2,000 in a savings account and earn an annual rate of return of 8%, how long does it take for it to grow to $5,000?

Answer: 12 years

Work:
2000 = 5000/ 1.08^t
tln1.08 = ln2.5
t = 11.9

You deposited an amount of money into a savings account that earns an annual rate of return of 9% and after 5 years the account has grown to $8,000. How much did you originally deposit?

Answer: 5,199

Work:
Vo = 8000/1.09^5 = 5 199

You are guaranteed to have $100 in one year. What is the future value of this $100 exactly one year from now. (The discount rate is 10%.)

Answer: 90.91

Work:
100 = Vo (1.1)
Vo = 90.91

 

[Denis]

1st one is correct; 876.76

Too lazy to check 'em all!