SOLUTION :
For continuously compounded case, we use the following formula :
FV = A e^(r t)
where,
FV = accumulated amount after t years.
A = amount deposited = $4000
r = rate of annual interest = 6% = 0.06
t = period of deposit in years.
a.
When t = 6 years:
FV
= 4000 * e^(0.06 * 6)
= 5733.32 ($) (ANSWER).
b.
When t = 9 years 9 months = 9.75 years
FV
= 4000 * e^(0.06 * 9.75)
= 7179.96 ($) (ANSWER).
c.
When t = 4 years 11 months 24 days = 4 + 11/12 + 24/365 = 4.98242 years
FV
= 4000 * e^(0.06 * 4.98242)
= 5393.74 ($) (ANSWER).
d.
When t = 20 years 213 days = 20 + 213/365 = 20.58356 years
FV
= 4000 * e^(0.06 * 20.58356)
= 13753.70 ($) (ANSWER).
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