Problema Solution
Sarah Wiggum would like to make a single investment and have $2.0 million at the time of her retirement in 35 years. She has found a mutual fund that will earn 4 percent annually. How much will Sarah have to invest today? If Sarah earned an annual return of 14 percent, how soon could she retire?
Answer provided by our tutors
A = $2,000,000.00 the future value
t = 35 years
r = 0.04 or 4% the annual rate
P = the principal
A = P(1 + r)^t
P = A/((1 + r)^t)
Plug the values:
P = 2000000/((1 + 0.04)^35)
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P = $506,830.942
Sara will have to invest $506,830.942 today.
If the annual return is r = 0.14 or 14%, the principal P = $506,830.942 and we need to find the time t:
2000000=506830.942((1 + 0.14)^t)
506830.942((1 + 0.14)^t) = 2000000
1.14^t = 2000000/506830.942
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t = 10.48 years
She could retire in 10.48 years.