I need help with this problem please.
Find the annual rate of growth (interest rate) on an account that was worth $150 in 1972 and $540.53 in 1994.
Let the interest rate be $\displaystyle x \%$, and the principal be $\displaystyle p$ then:Originally Posted by takkun0486
after 1 year you have: $\displaystyle (1+x/100)p$
after two years you have: $\displaystyle (1+x/100)^2p$
:
:
after $\displaystyle n$ years you have: $\displaystyle (1+x/100)^np$
Now 1972 to 1994 is 22 years, so we have:
$\displaystyle
540.53=(1+x/100)^{22}150
$
Which may be rewritten as:
$\displaystyle
1+x/100=(540.53/150)^{1/22}
$,
or:
$\displaystyle
x=100[(540.53/150)^{1/22}-1]
$
RonL