Question

find the monthly payment, P needed to have a sinking fund accumulate the future value, A, at time t. The yearly interest rate, r, is given. Interest is compounded monthly. Use the formula for finding the future value of an ordinary annuity. A= $10,000; r= 4.5%; t=3 years

Answer 1

let's use a(1+r/n)^nt
your compound interest formula
a=orginal amount
r= rate in decimal form
n=compounding periods per year
t=time in years
Now you can just plug it in, so (remember to turn percent into a decimal) (and when it's compounded monthly it means it's 12 times per year)
10,000 ( 1 + .045/12)^12*3
So let's solve using basic order of operations
10,000(1.00375)^36
plug this into your calculator you get some nasty stuff, but it's 11,442.48

Answer 2

annually= once per year n=1
quarterly= 4 times per year n=4
monthly= 12 times per year n=12
semi-annually= 2 times per year n=2

Answer 3

Thank you!

Answer 4

np :) ask me if you don't understand something

Answer 5

First get the monthly effective interest rate:

\[(1 + i_{12})^{12} = 1.045\]

Using that, plug it into this:

\[A = P{{(1+i_{12})^{3}-1\over{i_{12}}}}\]

Answer 6

nevrerforget this is an annuity, meaning monthy payments, so your method won't work.

Answer 7

thank you for all of your help!