(a) We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount after one year, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times compounded per year, and t is the time in years.
In this case, we have:
A = 4600(1 + 0.038/365)^(365*1)
A = $4,781.53
So the amount in the account after one year is $4,781.53.
(b) The effective annual interest rate takes into account the compounding effect. We can use the formula:
EAR = (1 + r/n)^n - 1
where EAR is the effective annual interest rate and all other variables are as defined above.
In this case, we have:
EAR = (1 + 0.038/365)^365 - 1
EAR = 0.0393 or 3.93%
So the effective annual interest rate is 3.93%.
Austin invested
$4600
in an account that pays an annual interest rate of
3.8%
, compounded daily. Assume there are
365
days in each year. Answer each part.
(a) Find the amount in the account after one year, assuming no withdrawals are made.
Do not round any intermediate computations, and round your answer to the nearest cent.
$
(b) Find the effective annual interest rate, expressed as a percentage.
Do not round any intermediate computations, and round your answer to the nearest hundredth of a percent.
1 answer
1 answer