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Use the information for the question(s) below
Use the information for the question(s) below. Assume that today is your 31st birthday and that you are planning on retirement at age 60. Your current salary is $65,000 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 on every birthday up to and including your 60th birthday. Your first contribution will be made today (on your 31st birthday) and will be 7% of your current salary. Likewise, you expect to deposit 7% of your salary each year until you reach age 60. Assume that the rate of interest is 9% APR with annual compounding. The future value (FV) at retirement (on your 60th birthday) of your savings is closest to: $709,198 $620,199 $452,257 $1,017,577 $895,448
Expert Solution
First Annual deposit, A= 7%*65000=$4550
g=5%
r=9%
n=30
FV= A*((1+r)^n-(1+g)^n)/(r-g)
=4550*((1+9%)^30-(1+5%)^30)/(9%-5%)
=4550*(1.09^30-1.05^30)/4%
=4550*(13.2677-4.3129)/0.04
=4550*8.9457/0.04
=1017577.48
Hence 4th option is correct
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