Question

Need Help!
Joanne starts to save at age 20 for a vacation home that she wants to buy for her 50th birthday. She will contribute $3000 each year to an account, which earns 2.4% annual interest, compounded quarterly. What is the future value of this investment, rounded to the nearest dollar, when Joanne is ready to purchase the vacation home?
$525,009

$528,159

$132,040

$131,252

Answer 1

@maddiegirl

Answer 2

Its C

Answer 3

@ElonaSushchik direct answers are not allowed

Answer 4

How did you figure that out?

Answer 5

@OGsupa stop stalking me! lol

Answer 6

PV = A/R - A/[R*(1+R)^N) <--- this is the formula I use

Answer 7

okay, could you show me what goes where xD sorry

Answer 8

If you knew the PV of the annual contributions, you could use the same formula. If the annual contributions are the same amount each year, then you can use the Annuity formula to find the PV of those contributions.

The formula for the PV of an annuity is:

PV = A/R - A/[R*(1+R)^N)

where R is the periodic yield, A is the periodic payment and N is the number of payments.


Let's look at an example. Suppose that you want to invest $25,000 now and you will contribute an extra $5,000 every year for 15 years. Suppose that the interest rate is 8% per year and it compounds quarterly. I made this more difficult to illustrate a point.

Let's find the PV. Since the annuity is annual, we need an annualized rate (annual effective rate). The 8% is nominal, not effective -- so we need to find a rate that includes te effects of compounding. The quarterly rate is 2% (one fourth of 8%) -- so we can get the annual rate by looking at:

R = 1.02^4 - 1.0 = 8.243216%

The annuity is for $5,000 per year, so the present value of that is:

5,000/0.08243216 - 5000/ [0.08243216*1.08243216^15] = $42,169.08

We need to add the $25,000 contribution we now make to get:

PV = $67,169

We can now calculate the future value in one of two ways -- compounding 2% quarterly or compounding 8.243216% annually.

FV = PV * 1.02)^60 = $220,383.83

If your annual contributions change from year to year -- it is best to do this in an Excel spreadsheet.

Answer 9

@ElonaSushchik next time cite that please :) TY

Answer 10

So do u get what i explained @0negaug3

Answer 11

you did not explain that @ElonaSushchik you need to cite that

Answer 12

yes a little bit! can you help me with like 3 more please?

Answer 13

Sure anytime!!!

Answer 14

if you don't break the coc