Question

Find the principal needed now to get the given​ amount; that​ is, find the present value.To get $ 90 after 2 and three fourths years at 6​% compounded continuouslyThe present value of $ 90 is $ nothing .​(Round to the nearest cent as​ needed.)

Answer 1

Explanation:

For continuous compounding, we use the following formula

$FV_{N} = PVe^{i N}$

Scenario 1 :

FV = $ 90

N = 2 years

I = 6%

PV= ?

$FV_{N} = PVe^{i N}$

$90 = PVe^{(0.06) (2)}$

$\frac{90}{e^{(0.06) (2)}} = PV$

$PV = 79.8228$

PV = $ 79.82

Scenario 2:

$FV_{N} = PVe^{i N}$

$90 = PVe^{(0.06) (3)}$

PV = $ 75.17

Scenario 3:

$FV_{N} = PVe^{i N}$

$90 = PVe^{(0.06) (4)}$

PV = $ 70.80