Math Help - Should I be using t = I/Pr ?

1. Should I be using t = I/Pr ?

Hello. In a maturity value interest question I am not quite sure what formula to use to get time, and also what measurement I should be using for the time (days, months, etc)

The question is:

Calculate the time period of an investment in a mutual fund that matured to $250,000 yielding an interest of$75,000 at 6% compounded semi-annually? Please round your answer up to the nearest month.

What I have done so far:

S = P + I so P=S-I P = 250,000-75,000 = 175,000

Now that I have S, P, and I, time is required.

I tried using t=i/pr which gets me 75,000 / [250,000*0.06] which = 5

Is that 5 years? Another thing is that equation didnt account for the semi annual compounding :s

Thanks

2. Re: Should I be using t = I/Pr ?

There are a few things wrong here. First, the formula t = i/pr works for simple interest only, not compound interest. And second, the denominator of that should be the amount invested, which was 175K. So that formula would yield t = 75/(175*.06) = 7.14, meaning it would take 7.14 years of simple interest to make the investment reach \$250K.

For compound interest you use: $FV = PV(1+i)^n$ where i is the interest rate per period and n is the number of periods of time. In this case a period is half a year in duration, and so the value for i is 0.06/2. PV is the present (or beginning) value and FV is the future (or ending) value. So you have:

$250 = 175(1+\frac {0.06} 2 )^n$

Do you know how to solve for n? Hint - it requires using logarithms. Once you have a value for n, round up to the next whole number and then multiply by 6 to get the number of months.