Answer:
A deposit of 36,922.02 dollars will be equivalent to the series of emergencies deposits of 2,000 starting today.
Explanation:
we need to know the future value of the emergencies deposit and then, calculate which lump sum can generate the same amount. As the deposit are done at the beginning It will be an annuity-due:
[tex]C \times \frac{(1+r)^{time} -1}{rate}(1+r) = FV\\[/tex]
C 2,000
time 36 (3 years x 12 months per year)
rate 0.045
[tex]2000 \times \frac{(1+0.045)^{36} -1 }{0.045}(1+0.045) = FV\\[/tex]
FV $180,082.6885
Now we calculate the lump sum which yield this amount as well:
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity $180,082.6885
time 36.00
rate 0.045
[tex]\frac{180082.68854409}{(1 + 0.045)^{36} } = PV[/tex]
PV 36,922.02
