Problema Solution
$15,000 is invested in each of two accounts, both paying 4% annual interest. In the first account, interest compounds quarterly, and in the second account, interest compounds daily. Find the difference between the accounts after 24 years. (Give your answer correct to the nearest cent.)
Answer provided by our tutors
P = $15,000 the principal (the money deposited)
r = 0.04 or 4% annual interest rate
t = 24 years
m = 3 compounding period per year (compounded quarterly)
i = r/m = 0.06/3 = 0.02 interest rate per period
n = t*m = 24*3 = 72 total number of compounding periods
A = future value
A = P(1 + i)^n
A = 15000(1 + 0.02)^72
A = $62,417.11
P = $15,000 the principal (the money deposited)
r = 0.04 or 4% annual interest rate
t = 24 years
m = 365 compounding period per year (compounded daily)
i = r/m = 0.06/365 interest rate per period
n = t*m = 24*365 = 8760 total number of compounding periods
A = future value
A = 15000(1 + 0.06/365)^8760
A = $63,300.97
the difference between the accounts is
63,300.97 - 62,417.11 = $883.86
after 24 years the second account will have $883.86 more then the first account.