Answer:
A quota of $ 583.388 every thre months is equivalent to these three deposits.
Explanation:
We need to first calculate the future value of the deposits
and then, we calculate the PMT which is equivalent
[tex]Principal \: (1+ r)^{time} = Amount[/tex]
First deposit:
Principal $ 7,000
time 28 (7 years x 4 quarter per year)
rate 0.02 (8% over 4 = 2% quarterly)
[tex]7000 \: (1+ 0.02)^{28} = Amount[/tex]
Amount 12,187.17
Second deposit:
[tex]6000 \: (1+ 0.02)^{16} = Amount[/tex]
Amount 8,236.71
Third deposit:
[tex]1500 \: (1+ 0.02)^{4} = Amount[/tex]
Amount 1,623.65
Total: 12,187.17 + 8,236.71 + 1,623.65 = 22,047.53
Now we solve for a PMT annuity-due (we are doing the first deposit at the beginning of the period)
[tex]PV \div \frac{(1+r)^{time} -1}{rate}(1+r) = C\\[/tex]
FV $22,047.53
time 28 (7 years 4 quar a year)
rate 0.02 (8% per year divide into 4 = 2% quarterly)
[tex]22047.53 \div \frac{(1+0.02)^{28} + 1 }{0.02}(1.02) = C\\[/tex]
C $ 583.388
