Use the given information to answer the questions for the CD

Use the given information to answer the questions for the CD.

(a) Each time interest is compounded, what is the percentage gain in the CD\'s value? (Round your answer to four decimal places.)
%

(b) What is the future value of the CD when it matures, assuming the minimum amount is invested? (Round your answer to two decimal places.)
$___________

(c) What is the average rate of change of the investment from the time when the CD is purchased until the time it matures? (Round your answer to two decimal places.)
$___________per year

(d) What is the APY for the CD? (Round your answer to two decimal places.)
APY =  %

(e) What initial investment would be required for the CD to be worth $5000 when it matures? (Round your answer to two decimal places.)
$___________

(f) How much more money would the CD be worth if the interest was compounded continuously instead of periodically? (Assume the minimum amount is invested. Round your answer to two decimal places.)

$___________

Solution

amount invested = $ 1000

rate = 2.86%

compounding monthly

time = 12 months

b) future value = present value* ( 1+ i/n)^ n

where i = interest rate

n = number of compounding periods

hence , future value = 1000( 1+ .0286/12)^12

future value = $1028.98

C) average rate of change = 1028.98 - 1000 = 28.98

d) APY = ( 1+ i/n)^n - 1

APY = ( 1+ .0286/12)^12 - 1

APY = .0289* 100 = 2.89 %