assume that the initial deposit is $20000 and the nominal annual interest rate is 5.7%. Determine the amount in the account in 10 years if the interest is compounded as follows (round your answers to the nearest dollar):
(a) Annually: P=20000(1.057)^10
(b) Monthly:
(c) Weekly (assume all years have 52 weeks):
(d) Daily (assume all years have 365 days):
(e) Continuously: P=20000e^(0.057*10)
I need help with how to do b-d!
Thanks!
for multiple periods per year, just divide the interest rate and multiply the number of years.
(b) P = 2000(1+.057/12)^(12*10)
and similarly for other divisions of the year into multiple parts.
To calculate the amount in the account for each compound frequency, you need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount in the account after t years
P = the initial deposit
r = the nominal annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
To solve the problem for parts (b) to (d), we will use this formula with different values for n.
(b) Monthly Compounding:
Since interest is compounded monthly, n = 12 (12 months in a year).
The formula becomes: A = P(1 + r/12)^(12*10)
(c) Weekly Compounding:
Since interest is compounded weekly, n = 52 (52 weeks in a year).
The formula becomes: A = P(1 + r/52)^(52*10)
(d) Daily Compounding:
Since interest is compounded daily, n = 365 (365 days in a year).
The formula becomes: A = P(1 + r/365)^(365*10)
Now, let's calculate each part:
(b) Monthly Compounding:
A = 20000(1 + 0.057/12)^(12*10)
(c) Weekly Compounding:
A = 20000(1 + 0.057/52)^(52*10)
(d) Daily Compounding:
A = 20000(1 + 0.057/365)^(365*10)
To solve these equations, you can use a calculator or a spreadsheet software. Plug in the values and raise the expressions to the required power. Finally, round your answers to the nearest dollar, as requested.