Question

Bella seeks to start her own business in 5 years. In order to have the required funding, she will need to accumulate an additional 200,000 in today's dollars. If you assume inflation will be 2% and can earn 8%annually after-tax, how much will she have to invest at the beginning of each year?

Answer 1

Here nominal rate = 8% , inflation rate = 2%

Real rate of interest = (1+nominal rate)/(1+inflation rate) - 1

=(1+8%)/(1+2%) - 1

(1.08)/(1.02)-1

=1.058824-1

=0.058824

=5.8824%

Now one wants 200,000 after 5 years, hence amount to be invested at begining of every year can be found using formula of future value of annuity due

FV(annuity due) = A[(1+r)^n - 1 /r] x (1+r)

Here r = 5.8824%

n = 5 years

Thus

200,000 = A[(1+5.8824%)^5 - 1/ 5.8824%] x (1+5.8824%)

200,000 = A[(1.058824)^5 - 1/0.058824] x (1.058824)

200,000 =A [1.330816 - 1 /0.058824] x (1.058824)

200,000 = A[ 0.330816/0.058824] x 1.058824

200,000 = A x 5.623822 x 1.058824

A = 33587.28$

Thus she will have to invest at the beginning of each year $33,587.28