Question

Need the answer of question 26

c. 6.07% 25. You are currently 30 years old and have $25,000 saved in an investment account. You plan to add $200 monthly beginning next month until you retire at the age of 75. The expected annual return from a balanced portfolio is 6%. How much will be in the account when you retire? a. $551,199 b. $791,243 c. $837,555 d. $854,700 e. $920,698 26. If prices increase 2% annually [the Federal Reserve's target for inflation] and your contributions remain unchanged, the purchasing power of your savings in current dollars, or its value in "real terms", will be: a. b. c. d. e. $552,683 $420,234 $411,804 $389,033 $377,667

Answer 1

25. Currently you have $25,000 for your retirement, therefore future value of deposit at time of retirement

FV = PV * (1+r %) ^n

Where,

Future value of deposit FV =?

Present value of deposit PV = $25,000

Interest rate = 6% per year or 6%/12 =0.5% per month

Time period n = 45 years (30 years – 75 years) = 45 years *12 = 540 months

Therefore

FV = $25,000 * (1 + 0.5%) ^540

= $369,499

Now we can again use FV of an Annuity due formula to calculate the future value of monthly savings of $200 from regular salary

FV = PMT*(1+i) *{(1+i) ^n−1} / i

Where FV =?

PMT = Monthly savings = $200 per month

n = N = number of payments = 45 years *12 = 540 months

i = I/Y = interest rate per year = 6% or 6%/12 =0.5% per month

Therefore,

FV = $200 *(1+0.5%) *{(1+0.5%) ^540−1} / 0.5%

FV = $551,199

Therefore future value of total savings at the time of retirement = $551,199 + $369,499

= $920,698

Therefore correct answer is option e. $920,698

26. Now if there is inflation rate of 2% for all these investment period then the real value of this savings or purchasing power in today’s dollar term can be calculated by discount the savings amount by 2% for 45 years

Value of savings in real term = Value of savings/ (1+ inflation rate) ^number of years

= $920,698 / (1+2%) ^45

= $377,667

Therefore correct answer is option e. $377,667