Thread: Annuities

a) Determine the present value on January 1, 2000, of payments of $200 every 6 months from January 1, 2000, through January 1, 2004, inclusive, and $100 every 6 months from July 1, 2004, through January 1, 2010, inclusive, if i = .06.

I think it might be something like: 100(a angle 8)(0.03) + 100(a angle 20)(0.03) which equals 100((1 - v^8)/0.03) + 100((1 - v^20)/0.03) , v=1/1.03
But the answer is $2,389.72 which is way off from what I'm getting. Am I even close?

b) At the beginning of the year Kelly establishes a fund with a deposit of $1000. At the beginning of each month a health club withdraws a $24 fee. The fund earns a nominal rate of interest of 18% compounded monthly. Determine the amount in the fund at the end of the year.

The only way I can think to do this is calculating each month separately so I know there's a faster way ... Any suggestions?

Thank you!!

Originally Posted by bart203

a) Determine the present value on January 1, 2000, of payments of $200 every 6 months from January 1, 2000, through January 1, 2004, inclusive, and $100 every 6 months from July 1, 2004, through January 1, 2010, inclusive, if i = .06.

I think it might be something like: 100(a angle 8)(0.03) + 100(a angle 20)(0.03) which equals 100((1 - v^8)/0.03) + 100((1 - v^20)/0.03) , v=1/1.03
But the answer is $2,389.72 which is way off from what I'm getting. Am I even close?

b) At the beginning of the year Kelly establishes a fund with a deposit of $1000. At the beginning of each month a health club withdraws a $24 fee. The fund earns a nominal rate of interest of 18% compounded monthly. Determine the amount in the fund at the end of the year.

The only way I can think to do this is calculating each month separately so I know there's a faster way ... Any suggestions?

Thank you!!

a) The first piece has 9 of those $200 payments. It's an annuity due.
a) Make up your mind on the number of $100 payments. It looks like 12 to me.
b) You must learn to use "Basic Principles".

if r = 1 + 0.18/12 = 1.015

At the end of the year, we have

1000r^12 -24(r^12 + r^11 + ... + r^1)

You should be able to add the 12 values in the parentheses and you will nearly be done.

Originally Posted by bart203

b) At the beginning of the year Kelly establishes a fund with a deposit of $1000. At the beginning of each month a health club withdraws a $24 fee. The fund earns a nominal rate of interest of 18% compounded monthly. Determine the amount in the fund at the end of the year.

Simply pretend this is a $1000 loan at monthly payments of $24,
rate .18/12 per month; what is loan balance after 12 payments?

Originally Posted by bart203

a) Determine the present value on January 1, 2000, of payments of $200 every 6 months from January 1, 2000, through January 1, 2004, inclusive, and $100 every 6 months from July 1, 2004, through January 1, 2010, inclusive, if i = .06.

Interest rate is WHAT? i = .06 means every 6 months, from .12/2 = .06;
get that straightened out.

With these, sometimes easier to "see" using future value:
1) future value of payments of $200 to Jan.1/04
2) future value of above to Jan.1/10
3) future value of payments of $100 for same period as in 2)
Add 'em up, calculate present value.