Question

5) During your four years at college, you decide to work at part-time jobs and put your earnings into an account to save for a one-year trip around the world after graduation. In your freshman and sophomore years (for the first two years), you are able to deposit $500 at the end of every three month into this account. In the junior and senior years (last two years). you are able to deposit $500 at the end of every month. How much money would you see in your account when you graduate at the end of four years if the account earns 12% annual interest? Hint: you can treat the two streams of CFs separately, and sum their values up once you figure out how much they'll each be worth at the end of the four years

Answer 1

Using the compound interest , the future value of money at given interest rate can be calculated with following formula -

$FV = P(1+r)^{t}$

where,

FV = future value

P = Present value (Deposit Amount)

r = interest rate

t = time

If deposit is a constant equal deposit then use following formula -

$FV = P\sum_{t=1}^{t} (1+r)^{t}$

We can also calculate the future using excel with =FV(rate,nper,pmt,0) formula.

Please refer to below spreadsheet for calculations

Formula reference -

Thus, Amount in Account after 4-year would be $ 17,932.90.