Question

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?

Answer 1

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

Step-by-step explanation:

This will be an arithmetic progression with h = 500

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

`e^(0.07) =(1+r)^(4)`

`\sqrt[4]{e^(0.07)}-1 = r__(quarter)`

r = 0.017654022

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

`C * ((1+r)^(time) -1 )/(rate) =FV\\`

C 1,100

time 36

rate 0.017654022

`1100 * ((1+0.0176540221507619)^(36) -1)/(0.0176540221507619) =FV\\`

FV $54,682.8156

plus future value of the increases:

`(h)/(i) ( S_(n:i)- n)`

500/0.017654022 = 28,322.15773

Sn:i

`1 * ((1+0.0176540221507619)^(36) -1)/(0.0176540221507619) = FV\\`

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