# Mathematical Interest Theory

• Nov 22nd 2012, 08:22 AM
ggarrison
Mathematical Interest Theory
Anurag receives an annuity that pays \$1000 at the end of each month. He wishes to replace it with an annuity that has the same term and has only one payment each year, and that payment should be at the beginning of the year. How much should the payments be if the exchange is based on a nominal discount rate of 3% payable quarterly?

I know that we're talking about at least one annuity immediate and one annuity due. Both of which I have the formulas for. I'm getting tripped up mostly on what interest rates to use where. Discount of 3% nominal payable quarterly means there's a discount rate of 0.75% every quarter. I know that to turn the discount into interest it's i=d/(1+d). (monthly interest I found to be 0.002570705, quarterly interest 0.0077319588, and yearly interest 0.0312883867).

My idea of a set-up (that has yet to work... 1000a im n(0.0077319588)/sn(0.0077319588) = P a due n(0.0312883867) where P is the payment amount of the new annuity.
• Nov 22nd 2012, 09:51 AM
HallsofIvy
Re: Mathematical Interest Theory
It would help if you would explain exactly what a "nominal discount rate of 3% payable quarterly" meant. And what formulas do you know related to this?
• Nov 22nd 2012, 12:07 PM
ggarrison
Re: Mathematical Interest Theory
I know that we're talking about at least one annuity immediate and one annuity due. Both of which I have the formulas for. I'm getting tripped up mostly on what interest rates to use where. Discount of 3% nominal payable quarterly means there's a discount rate of 0.75% every quarter. I know that to turn the discount into interest it's i=d/(1+d). (monthly interest I found to be 0.002570705, quarterly interest 0.0077319588, and yearly interest 0.0312883867).

My idea of a set-up (that has yet to work...) 1000a im n(0.0077319588)/sn(0.0077319588) = P a due n(0.0312883867) where P is the payment amount of the new annuity.