Some Interest problem

(1) A continuously paying level annuity pays $50 each year for ten years. The force of interest is (1+t) -1. Find the present value of this annuity. ?

(2) Stacey and her husband David have a joint savings account that earns 3.5% interest payable continuously and has a current balance of $58,458. Each year, David wishes to withdraw $4,000 payable continuously at a level rate. Stacey wishes to deposit X at the beginning of each year (for thirty years) so that the account will last for thirty years. What is the least X that will work?

(3) Bob deposits $1,500 at the beginning of each quarter for sixteen years in a fund earning a nominal rate of interest of 6% convertible monthly. The interest from this fund is paid out monthly and can only be reinvested at an effective annual rate of 5.2%. This is just as in Problem (4.5.5). Find Bob?s yield rate for the twenty-year period.

(4) Payments of $5,000 are made into a fund at the beginning of each year for ten years. The fund is invested at an annual effective rate of i. The interest generated is reinvested at 10%. The total accumulated value at the end of the ten years is $100,000. Find i .

(5)

\fWhen eemputed using an effective interest rate of i , it is kncrwn that the present value of $2,000 at the end of each year for 2H years plus an additional 15 1,000 at the end of each of the rst a years is $52,800. Using this same interest rate, the present value of an a year deferred armuityimmediate paying $4,000 per year fur n years is $21400. Find a. [I-IINT: First nd am,- and am,- , then a" and E .]