Question

Suppose ​$21 comma 00021,000 is invested at an annual rate of 77​% for 1313 yearsyears. Find the future value if interest is compounded as follows. a. Annually b. Quarterly c. Monthly d. Daily​ (365 days) e. Continuously

Answer 1

Annually 50,606.75

Quarterly 51, 761.76

Daily ​ 52,166.22

Continuously 52,170.77

Step-by-step explanation:

We have to use the future value for different compounding:

Annually:

`Principal \: (1+ r)^(time) = Amount`

Principal 21,000.00

time 13.00

rate 0.07000

`21000 \: (1+ 0.07)^(13) = Amount`

Amount 50,606.75

Quarterly:

`Principal \: (1+ r)^(time) = Amount`

time 52.00 (13 years x 4 quarter per year)

rate 0.01750 ( 7% over 4 quarters)

`21000 \: (1+ 0.0175)^(52) = Amount`

Amount 51,761.76

Daily (365 days):

`Principal \: (1+ r)^(time) = Amount`

time 4,745 (13 years x 365 days per year

rate 0.00019 (0.07 / 365)

`21000 \: (1+ 0.000191780821917808)^(4745) = Amount`

Amount 52,166.22

Continuously:

`Principal \: e^(rate * time) = Amount`

`21000 \: e^(0.07 * 13) = Amount`

Amount 52,170.7732