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Assume that you are 30 years old today, and that you are planning on retirement at age 65
Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your current salary is $45,000 and you expect your salary to increase at a rate of 5% per year as long as you work. To save for your retirement, you plan on making annual contributions to a retirement account. Your first contribution will be made on your 31st birthday and will be 8% of this year's salary. Likewise, you expect to deposit 8% of your salary each year until you reach age 65. Assume that the rate of interest is 7%. The future value at retirement (age 65) of your savings is:
Expert Solution
Deposit in year 1 or 31st birthday = 45000 x (1+5%) x 8%
= $3,780
PMT = Deposit in first year;
R = Interest rate;
G = Growth rate of deposit wrt salary;
N = Years
Future value of growing annuity:
FV = PMT x (((1+R)^N-(1+G)^N)/(R-G)
FV = 3780 x (((1+7%)^35-(1+5%)^35)/(7%-5%)
FV at retirement age of 65 = $975,347
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