Problema Solution
Brian wants to have $7000 in the bank in 10 years. He deposits $3000 today at 8% interest compounded semiannually. How much additional money will he need to reach the desired $7000.
Answer provided by our tutors
P = $3,000 the principal
r = 0.08 or 8% annual interest rate
m = 2 compounding period per year (compounded semiannually)
i = r/m = 0.08/2 = 0.04 interest rate per period
t = 10 years
n = t*m = 10*2 = 20 total number of compounding periods
A = the future value (the amount in the account after t years)
A = P(1 + i)^n
A = 3000*(1 + 0.04)^20
........
........
A = $6,573.37
$7,000 - $6,573.37 = $426.63
Brain will need $426.63 additional money to reach the desired $7,000.