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.
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.
Principal
Rate
Time
$1006
1.6%
2 years
Question content area bottom
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.)
1 answer