Asked by Lara
If $20,000 is invested at an annual rate r (expressed as a decimal) compounded monthly, the total amount (principal P and interest) accumulated after 10 years is given by the formula A=10000(1+r/52)^520Find the rate of change of A with respect to r. Find the percentage rate of change of A with respect to r when r = 0.06 (that is, 6%)
Answers
Answered by
oobleck
sorry. That formula is for weekly compounding. But, using it, we get, using the chain rule, d/dr u^n = n u^(n-1) du/dr
dA/dr = 10000*520(1+r/52)^519 * 1/52 = 100,000(1+r/52)^519
so plug in your numbers.
then use that to find the % rate of change as usual
dA/dr = 10000*520(1+r/52)^519 * 1/52 = 100,000(1+r/52)^519
so plug in your numbers.
then use that to find the % rate of change as usual
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