Answer:
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:
[tex]e^{0.07} =(1+r)^{4}[/tex]
[tex]\sqrt[4]{e^{0.07}}-1 = r__{quarter}[/tex]
r = 0.017654022
Then we calculate future value of an ordinary annuity of 1,100
[tex]C \times \frac{(1+r)^{time} -1 }{rate} =FV\\[/tex]
C 1,100
time 36
rate 0.017654022
[tex]1100 \times \frac{(1+0.0176540221507619)^{36} -1}{0.0176540221507619} =FV\\[/tex]
FV $54,682.8156
plus future value of the increases:
[tex]\frac{h}{i} ( S_{n:i}- n)[/tex]
500/0.017654022 = 28,322.15773
Sn:i
[tex]1 \times \frac{(1+0.0176540221507619)^{36} -1}{0.0176540221507619} = FV\\[/tex]
FV 49.7117
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
