Occasionally a savings account may actually pay interest compounded continuously. For each​ deposit, find the interest earned if interest is compounded​ (a) semiannually,​ (b) quarterly,​ (c) monthly,​ (d) daily, and​ (e) continuously. Use 1 year=365 days.

Question

Principal
Rate
Time
​$1006
1.6​%
2 years
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Part 1
​(a) The interest earned if interest is compounded semiannually is ​$enter your response here.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

Answer 1

The formula used to calculate the interest earned for each compounding period is:

A = P(1 + r/n)^(nt) - P

Where:
A = the final amount
P = the principal
r = interest rate (in decimal form)
n = number of times interest is compounded per year
t = time in years

Given:
P = $1006
r = 1.6% or 0.016 (in decimal form)
t = 2 years

For semiannual compounding (n = 2), the calculation becomes:

A = 1006(1 + 0.016/2)^(2*2) - 1006

A = 1006(1.008)^(4) - 1006

A = 1006(1.032236864) - 1006

A = 1037.733077504 - 1006

A = 31.733077504

The interest earned if interest is compounded semiannually would be approximately $31.73.