Answer:
Annually 50,606.75
Quarterly 51, 761.76
Daily 52,166.22
Continuously 52,170.77
Explanation:
We have to use the future value for different compounding:
Annually:
[tex]Principal \: (1+ r)^{time} = Amount[/tex]
Principal 21,000.00
time 13.00
rate 0.07000
[tex]21000 \: (1+ 0.07)^{13} = Amount[/tex]
Amount 50,606.75
Quarterly:
[tex]Principal \: (1+ r)^{time} = Amount[/tex]
time 52.00 (13 years x 4 quarter per year)
rate 0.01750 ( 7% over 4 quarters)
[tex]21000 \: (1+ 0.0175)^{52} = Amount[/tex]
Amount 51,761.76
Daily (365 days):
[tex]Principal \: (1+ r)^{time} = Amount[/tex]
time 4,745 (13 years x 365 days per year
rate 0.00019 (0.07 / 365)
[tex]21000 \: (1+ 0.000191780821917808)^{4745} = Amount[/tex]
Amount 52,166.22
Continuously:
[tex]Principal \: e^{rate \times time} = Amount[/tex]
[tex]21000 \: e^{0.07 \times 13} = Amount[/tex]
Amount 52,170.7732
