Problema Solution
Sarah Wiggum would like to make a single investment and have $2 million at the time of her retirement in 35 years. She has found a mutual fund that will earn 4% annually. How much will Sarah have to invest today? What if Sarah were a finance major and learned how to earn a 14% annual return? How soon could she then 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
How much will Sarah have to invest today?
A = P(1 + r)^t
P = A/((1 + r)^t)
P = 2000000/((1 + 0.04)^35)
P = $506,830.942
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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
2,000,000=506,830.942((1 + 0.14)^t)
t = (ln (2000000/506830.942))/ ln (1.14)
t = 10.48 years
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She could retire in 10.48 years.