# Financial Math FM/Problems

Problem 1
Drago deposits 100 into an account at the beginning of each 2-year period for 40 years. The account credits interest at an interest rate of i.

The accumulated amount in the account at the end of the 40 years is 3 times the accumulated amount in the account at the end of 20 years.

Calculate i.

Solution
${\displaystyle {s}_{\overline {20|}}=3{s}_{\overline {10|}}}$
${\displaystyle {\frac {((1+i)^{20}-1)}{i}}=3{\frac {((1+i)^{10}-1)}{i}}}$
${\displaystyle (1+i)^{20}-3(1+i)^{10}+2=0}$
${\displaystyle ((1+i)^{10}-1)((1+i)^{10}-2)=0}$
${\displaystyle (1+i)^{10}=2}$
${\displaystyle (1+i)=1.07177}$
${\displaystyle i_{annual}=.035}$