Answer:
Part A
[tex]A = 5280 (1.0035)^{12t}[/tex]
Part B
[tex]\$7,384.18[/tex]
Step-by-step explanation:
We are given
Principal P = $ 5280
Annual Interest Rate in percent, R = 4.2%
Compounded Monthly
First we convert R to a decimal by dividing by 100
Annual rate = 4.7/100 = 0.047
Then we divide by 12 to get the monthly rate of interest r
r = 0.042/12
r = 0.0035
The formula for amount accrued when compounded monthly is
[tex]A = P(1 + r)^{12t}[/tex]
where r is the monthly interest rate and t is number of years. we have 12 t in the exponent since there are 12 compounding periods in each year for a total of 12t periods
Plugging in values for the given problem the answers are
Part A
[tex]A = 5280 (1 + 0.0035)^{12t}\\\\A = 5280 (1.0035)^{12t}[/tex]
Part B
Substitute t = 8 in the above formula to get
[tex]A = 5280(1.0035)^{12\cdot8}\\\\A = 5280(1.0035)^{96}\\\\A = \$7,384.18\\\\[/tex]
