5. Tom has been saving 20% of his take-home salary every month, for the last 10 years, in an investment that yields 12% interest rate compounded monthly. His take-home salary in the first year was $3,000 per month, and it has increased annually by 5% over the 10 years. What is the current worth of Toms savings?
$3000/month = $36000/year
He saves 20%, so the value of the initial savings annuity is:
Ao = (0.2)36000
= $7200
The 12% interest is compounded monthly, so I need to get this in an annual form:
ie = (1 + is)m 1
= (1 + 0.12/12)^12 1
= 0.1268%
Adjusting the interest for the annual raise:
io = (1 + 0.1268)/(1 + 0.05) 1
= 0.0731
Now I have everything in terms of what he is saving on an annual basis. I can simply use the geometric gradient to calculate the present worth of his savings.
P = 7200(1.0731^10 1)/(0.0731* 1.0731^10 * 1.05)
= $47479.06