Question
In: Accounting
Under the NBA deferred compensation plan, payments made at the end of each year accumulate up...
Under the NBA deferred compensation plan, payments made at the end of each year accumulate up to retirement and then retirees are given two options. Option 1 allows the retiree to select the amount of the annual payment to be received, and option 2 allows the retiree to specify over how many years payments are to be received. Assume Hardaway has had $6,100 deposited at the end of each year for 30 years, and that the long-term interest rate has been 7%. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)
Required:
a. How much has accumulated in Hardaway's deferred
compensation account?
b. How much will Hardaway be able to withdraw at
the beginning of each year if he elects to receive payments for 16
years?
c. How many years will Hardaway be able to receive
payments if he chooses to receive $66,000 per year at the beginning
of each year?
Solutions
Expert Solution
a
| FV of annuity | = | P * [ (1+r)^n -1 ]/ r | |
| Periodic payment | P= | $ 6,100.00 | |
| rate of interest per period | r= | ||
| Rate of interest per year | 7.0000% | ||
| Payment frequency | Once in 12 months | ||
| Number of payments in a year | 1.00 | ||
| rate of interest per period | 0.07*12/12 | 7.0000% | |
| Number of periods | |||
| Number of years | 30 | ||
| Number of payments in a year | 1 | ||
| Total number of periods | n= | 30 | |
| FV of annuity | = | 6100* [ (1+0.07)^30 -1]/0.07 | |
| FV of annuity | = | 576,210.80 |
Answer is:
576,210.80
b
| Payment from today | = | FV/ [(1+r) * [ (1+r)^n -1 ]/r] | ||
| Future value | FV= | 576,210.80 | ||
| Rate of interest per period | r= | |||
| Rate of interest per year | 7.0000% | |||
| Payment frequency | Once in 12 months | |||
| Number of payments in a year | 1.00 | |||
| rate of interest per period | 0.07*12/12 | 7.0000% | ||
| Number of periods | n= | |||
| Number of years | 16 | |||
| Number of payments in a year | 1 | |||
| Total number of periods | n= | 16 | ||
| Annuity due | = | 576210.8/[ (1+0.07) * 8 [ (1+0.07)^ 16 -1] /0.07] | ||
| = | 19,309.87 |
Answer is:
19,309.87
c
| n | Number of payments required = | Log [ 1/ [1 - PV× r/ P] ]/ Log(1+r) | ||
| PV = | Present value | $ 510,210.80 | ||
| P= | Periodic payment | 66,000.00 | ||
| r= | Rate of interest per period | |||
| Annual interest | 7.00% | |||
| Number of payments per year | 1 | |||
| Interest rate per period | 0.07/1= | |||
| Interest rate per period | 7.000000% | |||
| Number of payments = | Log [ 1/ (1- 510210.8 × 0.07/66000) ]/ Log( 1+ 0.07) | |||
| n= | Number of payments = | 11.51 |
Total payments = 11.51 + 1 payment at beginning = 12.51 years
please rate.
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