grace deppsits $1000 in a.mutual fund earning 9.5% annual interest,compounded monthly  1.) write an exponential function thats model thid situation where y is the amount of grace imvestment and x...

grace deppsits $1000 in a.mutual fund earning 9.5% annual interest,compounded monthly 

1.) write an exponential function thats model thid situation where y is the amount of grace imvestment and x is the time in years

Asked on by wanda9

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steveschoen | College Teacher | (Level 1) Associate Educator

Posted on

Hi, Wanda.  I hope this helps.

The formula for compound interest problems is:

y = P (1 + r/n)^(xn)

y = final amount

P = Initial amount, what you start out with ($1000)

r = percent rate; don't forget to convert (9.5% = 0.095)

n = number of compounding periods per year

     monthly, n = 12

     bi-annually, n = 2

     quarterly, n = 4

x = time in years

So, plugging in the numbers we are given:

y = P (1 + r/n)^(xn)

y = 1000(1 + 0.095/12)^(12x)

The parenthesis with the addition can be simplified.  Do 0.095/12 first, then add 1.  That gives us:

y = 1000(1.0079167)^(12x), rounding to 7 decimal places

We could go further.  But, normally, I don't think most teachers do.  Going further, we would do "1.0079167^12" only, giving us:

y = 1000(1.099)^x, rounding to 3 decimal places

We can't do anything past that, Wanda.  Sorry.  I hope this will assist.  Good luck.

Steve

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