Question

Bradley invested an average of $550 per month since age 49 in various securities for his retirement savings. His investments averaged a 7% annual rate of return until he retired at age 73. Given the same monthly investment and rate of return, how much more would Bradley have in his retirement savings had he started investing at age 40? Assume monthly compounding.

Answer 1

$440,088.67
$63,558.00
$1,344,425.69
$282,480.00

Answer 2

@jim_thompson5910

Answer 3

you will use the FVOA formula (FVOA = future value of annuity)

Answer 4

find the FVOA for when he starts at age 49 and goes til age 73

then find the FVOA for when he starts at age 40 and goes til age 73

and take the difference of the two

Answer 5

oh sry, FVOA = future value of ordinary annuity

but same steps will be taken to get the answer

Answer 6

that formula is the FVOA= C((1+i)^nt) / i

Answer 7

yes, C is the monthly contribution

so C = 550

i = r/n = 0.07/12 = 0.00583 (compounding monthly)

n = 12 (compounding monthly)

t = number of years

Answer 8

t = 33?

Answer 9

or does t =9?

Answer 10

neither of those are right :(

Answer 11

when you go from age 40 to age 73, the value of t is 33 (73 - 40 = 33)

when you go from age 49 to age 73, the value of t is 24 (73 - 49 = 24)

Answer 12

so you need to find FVOA when t = 33 and when t = 24

then subtract the FVOA values

Answer 13

ohh! okay

Answer 14

i got 439583. but it's really close to one of my answers

Answer 15

Try it again. The answer I get is one of the answer choices.

Answer 16

btw, the formula you are working with is

\[\Large FVOA = C*\frac{(1+i)^{nt}-1}{i}\]

Answer 17

You said before that it was " FVOA= C((1+i)^nt) / i" but there should be a -1 up top and I missed that as well. But it's fixed now.

Answer 18

thats what it was haha i forgot the -1 oops

Answer 19

i got 439883?

Answer 20

when t = 33, you should get FVOA = 849234.96

Answer 21

check your work again

Answer 22

for that i got 848482. i probably put in a wrong number or something.

Answer 23

and for the t=24 i got 408,899

Answer 24

what are you typing in for t = 33?

Answer 25

550((1+.00583)^396 -1) / .00583

Answer 26

maybe you need to use more decimal digits?

If you do,

550((1+.005833333)^396 -1) / .005833333

you should get

849234.88

Answer 27

it's probably better to replace .005833333 with 0.07/12

Answer 28

doing that gives

550((1+0.07/12)^396 -1) / (0.07/12) = 849,234.96

Answer 29

yeah that worked

Answer 30

do the same for t = 24, what do you get?

Answer 31

408490

Answer 32

I'm getting 409146.29 for t = 24

Answer 33

hmm not sure how you got that, did you do

550((1+0.07/12)^288-1) / (0.07/12)

or no?

Answer 34

what do you get when you compute 550((1+0.07/12)^288-1) / (0.07/12)