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.

Question

jdoe0001 · Answer

use the "compound interest" equation to solve

recall that the balance for the compound interest is 
$\bf B = p\left(1+\frac{r}{n}\right)^{nt}\ \quad \
B = balance\
p = principal(deposit)\
r = rate\textit{ in decimals, }8\% = 0.08\
n = \textit{periods per year, semi-annual means, twice a year}\
t = years\ \quad \
\textit{he needs more than 3000, so 3000+a}\
B = (p+a)\left(1+\frac{r}{n}\right)^{nt}\implies 
7000 = (3000+a)\left(1+\frac{0.08}{2}\right)^{2\cdot 10}$

solve for "a", which is the "additional amount" for the deposit, to get a Balance of $7000