$$

$($

Complex present value

$$

$)$

$$You would like to have

$$

$

$4$

$3$

$$comma

$0$

$0$

$0$

$$in

$1$

$6$

$$years$.$ To accumulate this

$$

$$amount$,$ you plan to deposit each year an equal sum in the

$$

$$bank$,$ which will earn

$6$

$$percent interest compounded annually. Your first payment will be made at the end of the year.

a

$.$

$$How much must you deposit annually to accumulate this

$$

$$amount$?$

b

$.$

$$If you decide to make a large

$$

$$lump

$-$

sum deposit today instead of the annual

$$

$$deposits$,$ how large should this

$$

$$lump

$-$

sum deposit

$$

$$be

$?$

$($

Assume you can earn

$6$

$$percent on this

$$

$$deposit$.$

$)$

c

$.$

$$At the end of

$4$

$$years you will receive

$$

$

$8$

$$comma

$0$

$0$

$0$

$$and deposit this in the bank toward your goal of

$$

$

$4$

$3$

$$comma

$0$

$0$

$0$

$$at the end of

$1$

$6$

$$years$.$ In addition to this

$$

$$deposit$,$ how much must you deposit in equal annual deposits to reach your

$$

$$goal$?$

$($

Again assume you can earn

$6$

$$percent on this

$$

$$deposit$.$

$)$

Question content area bottom

Part

$1$

a

$.$

$$How much must you deposit annually to accumulate

$$

$

$4$

$3$

$$comma

$0$

$0$

$0$

$$in

$1$

$6$

$$

years

$?$

$$

$

$$

$$

enter your response here

$$

$($

Round to the nearest

$$

$$cent$.$

$)$