$0.$ How much more is a perpetuity of $$1,000$ worth than an annuity of the same amount for

$20$ years? Assume an interest rate of $10\%$ and cash flows at the end of each period. $$1,486\mathrm{.}44$

$31.$ Assume the total expense for your current year in college equals $$20,000.$ How much

would your parents have needed to invest $21$ years ago in an account paying $8\%$ compounded

annually to cover this amount? $$3,973\mathrm{.}11$

$32.$ The present value of an annuity stream of $$100$ per year is $$614$ when valued at a $10\%$

rate. By approximately how much would the value change if these were annuities due? $$61\mathrm{.}40$

Explain pls with formulas