An investor wants to analyze the earnings of a mutual fund account. Seven years ago, the value of the account was $17,000 and it is now worth $21,250 (no additional deposits were made). If the account is compared to a bank account paying interest that is compounded continuously, what interest rate would the bank account have to pay to match the mutual fund accounts earnings?

Question

An investor wants to analyze the earnings of a mutual fund account. Seven years ago, the value of the account was $17,000 and it is now worth $21,250  (no additional deposits were made). If the account is compared to a bank account paying interest that is compounded continuously, what interest rate would the bank account have to pay to match the mutual fund accounts earnings?

anonymous · Answer

A=Pe^(rt)
t=7
P= 17000
A=21250
just solve for r and replace the values

anonymous · Answer

but what about "m"? isn't the formula for it A=P(1+r/m) ^m*t

anonymous · Answer

I can't quite figure out what number to put for "continuous compounding".

anonymous · Answer

the problem says
compounded continuously,
so the formula is 
A=Pe^(rt)
this other formula 
A=P(1+r/m) ^m*t
is for interest compounded

anonymous · Answer

OH!!

jdoe0001 · Answer

$$
A(t)=Pe^{rt}\
A= principal= 21250\
P17000\
t=7\
21250=17000e^{7r}\
--------------------\
ln(21250)= \color{blue}{ln(17000e^{7r}) \implies ln(17000)+ln(e^{7r})}\
ln(21250)-ln(17000)=7r
$$

jdoe0001 · Answer

I think you can get "r" from there :|

jdoe0001 · Answer

I meant to say P=17000, btw :|

anonymous · Answer

so if it said it was a daily compound you would use the formula I had put originally and "m" would be 365, right?

jdoe0001 · Answer

@hvb91  then the 'day' would be the 'period', and for a 365 lifetime, yes

jdoe0001 · Answer

a period can be any arbitrary term really, 2 months, a year, a month