Question

Robert has determined he will need $80,000 at the beginning of each year after he retires. He expects to earn 5.0% on his funds after retirement, In addition, he wishes to leave $100,000 to the local Humane Society upon his death which will occur 25 years after he retires.

Robert will wok for 45 years before he retires. During his working years, robert will earn 10% on his investments.

1. Calculate the total funds Robert must have on the day he retires in order to meet his financial goals.

2. Calculate the monthly investment that Robert must make to meet his goals.

3. Imagine that Robert has $5,000 that he can invest today to start off his retirement fund. How much must he now save every month?

Round answers to nearest dollar and do NOT enter dollar signs.

Answer 1

PV of annuity for making pthly payment-Annuity Due
P = PMT+PMT x (((1-(1 + r) ^- (n-1))) / r)
Where:
P = the present value of an annuity stream	To be computed
PMT = the dollar amount of each annuity payment	80000
r = the effective interest rate (also known as the discount rate)	5%
n = the number of periods in which payments will be made	25
PV of retirement withdrawals=	PMT+PMT x (((1-(1 + r) ^- (n-1))) / r)
PV of retirement withdrawals=	80000+80000*(((1-(1 + 5%) ^- (25-1))) / 5%)
PV of retirement withdrawals=	1,183,891
PV of fund left for society=	100000/(1+5%)^25
PV of fund left for society=	29,530
So total funds needed at the time of retirment=	1183891+29530
So total funds needed at the time of retirment=	1,213,422
This fund will be accumulated by monthly contributions
FV of annuity
P = PMT x ((((1 + r) ^ n) - 1) / i)
Where:
P = the future value of an annuity stream	1,213,422
PMT = the dollar amount of each annuity payment	P
r = the effective interest rate (also known as the discount rate)	10.47%	((1+10%/12)^12)-1)
i=nominal Interest rate	10.00%
n = the number of periods in which payments will be made	45
FV of annuity=	PMT x ((((1 + r) ^ n) - 1) / i)
1,213,421.62	=PMT * ((((1 + 10.47%) ^ 45) - 1) / 10%)
Annual payment=	=1213421.62/((((1 + 10.47%) ^ 45) - 1) / 10%)
Annual payment=	1,389
Monthly deposit=	116
If initially 5000 are invested then FV of this amount at retirement=	5000*(1+10%)^45
If initially 5000 are invested then FV of this amount at retirement=	364,452
Remaining funds to be accumulated through monthly deposit=	1213421.62-364452.42
Remaining funds to be accumulated through monthly deposit=	848,969
FV of annuity=	PMT x ((((1 + r) ^ n) - 1) / i)
848,969.20	=PMT * ((((1 + 10.47%) ^ 45) - 1) / 10%)
Annual payment=	=848969.20/((((1 + 10.47%) ^ 45) - 1) / 10%)
Annual payment=	972
Monthly deposit=	81