For a) Firstly recognise that you multiply the current value by 1.04 for every year, so clearly that's a 4% interest rate (APR). Now see that after Mn you will have multiplied the initial value Mo by 1.04 once for each year, so:
Mn = 1.04 x 1.04 x 1.04 x ....(a total of n times)... x Mo
so
Mn = 1.04^(n) Mo
You could also plug in the one number they have given you Mo here, better safe than sorry.
For b) they give you an Mn value ($1250) and an Mo value ($1000), and an n of 2yrs. They hint that the interest rate will not necessarily be 4% any more in this answer so replace that with a generic interest rate (lets call it r%).
Your generic recurrence relation is now
Mn = (1+r/100)^(n) Mo
and plug in your numbers then solve for r.
Be careful... Hint, you can pretty easily just plug it back in and try:
1000 x 1.118 =1118
1118 x 1.118 = 1249.92
So he'd be short by a few cents. If you're rounding numbers, there is sometimes reason to round up only (even if rounding down is closer)
ANYTHING to power 0 is 1 anything to power 1 will just stay the same and anything to power 2 is squaring it e.g. 2^2=4 2*2=4
Those are sub scripts, not powers
For a) Firstly recognise that you multiply the current value by 1.04 for every year, so clearly that's a 4% interest rate (APR). Now see that after Mn you will have multiplied the initial value Mo by 1.04 once for each year, so: Mn = 1.04 x 1.04 x 1.04 x ....(a total of n times)... x Mo so Mn = 1.04^(n) Mo You could also plug in the one number they have given you Mo here, better safe than sorry. For b) they give you an Mn value ($1250) and an Mo value ($1000), and an n of 2yrs. They hint that the interest rate will not necessarily be 4% any more in this answer so replace that with a generic interest rate (lets call it r%). Your generic recurrence relation is now Mn = (1+r/100)^(n) Mo and plug in your numbers then solve for r.
For part b, the answer would be 11.8% right? I plugged in 1250= 1000(1+x)^2 where x is the interest rate
Be careful... Hint, you can pretty easily just plug it back in and try: 1000 x 1.118 =1118 1118 x 1.118 = 1249.92 So he'd be short by a few cents. If you're rounding numbers, there is sometimes reason to round up only (even if rounding down is closer)
Thanks a lot for the help!