You make a series of quarterly deposits every quarter starting at the end quarter 1 and ending at the end of quarter 36. the first deposit is $1,100, and each deposit increases by $500 each quarter. the nominal annual interest rate is 7%, and is compounded continuously. what is the future value of these series of deposits at the end of quarter 36?

the fund will be valued after 36 quarters: 443.027,75

Explanation:

This will be an arithmetic progression with h = 500

the continously rate we are going to convert to a quarterly equivalent rate:

r = 0.017654022

Then we calculate future value of an ordinary annuity of 1,100

C     1,100

time36

rate0.017654022

FV$54,682.8156

plus future value of the increases:

500/0.017654022 = 28,322.15773

Sn:i

FV49.7117

n =   36

Sn:i - n = 13.7117

$28,322.15773 x 13.7117 = $388.344,93

Now we add both:

$54,682.8156 + $388.344,93 = 443.027,75

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