As of April 19, 2017, the average annual \"jumbo\" interest rate for a bank cert

Question

As of April 19, 2017, the average annual "jumbo" interest rate for a bank certificate of deposit (CD) that is held for 5 years is 0.95% (that's 0.0095 as a decimal sad, right?) Using Example 7.3.1 in zyBooks as a guide, if the bank applies interest only once a year how much will $15,000 deposited into a CD be worth in 5 years? What would the same CD be worth if the interest were compounded quarterly (4 times a year)? What would the same CD be worth if the interest were compounded daily (assume 365 days in a year)?

Explanation / Answer

P = $15000

r = 0.95% = 0.0095

The popular formula for calculating annual compound interest is V = P(1+r/n)(nt)

V = the future value of the investment
P = the principal investment amount
r = the annual interest rate
n = the number of times that interest is compounded per year
t = the number of years the money is invested for

n = number of componding periods per year

So,

V = 15000 * (1 + 0.095/1)5

V = $15,726.17

When compounded 4 times a year, here n = 4

V = 15000 * (1 + 0.095/4)(5*4)

V = $15,728.81

When compounded daily, here n = 365

V = 15000 * (1 + 0.095/365)(5*365)

V = $15,729.68

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