An investor wants to analyze the earnings of a mutual fund account. Four years ago, the value of the account was and it is now worth (no additional deposits were made).

Question

An investor wants to analyze the earnings of a mutual fund account. Four years ago, the value of the account was and it is now worth (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?

Interest Rate ≈

Answer 1

Hi Hadassah,

You didn't provide numbers to solve the problem, but I can explain how to do it.

A mutual fund account typically increases in value over time, but it's not a fixed interest rate, and there is NO formula for the amount of money in this account. We can only assume what they have told us about the value 4 years ago and the value now.

A bank account paying interest compounded continuously DOES have a formula. This one:

A=Pe^rt

where,

A=ending amount

P=starting amount

e=Euler's number

r=interest rate (as a decimal)

t=elapsed time

So, simply use this equation to plug in known values and solve for the interest rate.

A = your value four years ago.

P = your value now

e= 2.71828

r=interest rate

t=4

Hope this helps! :)

Answer 2

Let Vb be the earlier value of the asset, and Va be the value of the asset 4 years later. Expressing the interest rate r as a fraction (not as a percentage), we have Va=Vb*exp(rt)=Vb*exp(4r) after four years of continuous compounding at the annual rate of r. Solving for r gives (1/4)ln(Va/Vb)=r. To express this as a percentage, multiply by 100 to get 25*ln(Va/Vb).