you would like to have $800,000 when you retire in 35 years. How much should you invest each quarter if you can earn a rate of 6.7% compounded quarterly?

a) How much should you deposit each quarter?

b) How much total money will you put into the account?

c) How much total interest will you earn?

i = .067/4 = .01675

n = 140
P(1.01675^140 - 1)/.01675 = 800,000
p = .....

b) multiply p by 140
c) subtract 800,000 - answer to b)

Don't understand?

Can you help I don't understand. Thanks

You do these kind of questions, you MUST know the basic formulas.

I used
Amount = payment( (1+i)^n - 1)/i

I you don't know this, how can you possibly handle this topic of annuities?

What's the answer?

To determine how much you should invest each quarter, you can use the formula for calculating the future value of an investment:

FV = P(1 + r/n)^(nt)

where:
FV = future value
P = initial deposit or investment
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years

In this case, you want to have $800,000 when you retire in 35 years. The interest rate is 6.7% compounded quarterly.

a) To find out how much you should deposit each quarter, we can rearrange the formula. Let's solve for P:

800,000 = P(1 + 0.067/4)^(4 * 35)

To calculate this, we can use a financial calculator, spreadsheet software, or an online financial tool. Plugging the values into an online calculator, it tells us that we need to deposit approximately $262.21 each quarter.

b) To calculate the total amount of money you will put into the account, multiply the quarterly deposit amount by the number of quarters:

Total deposits = Quarterly deposit amount * Number of quarters

Total deposits = $262.21 * 35 * 4 = $36,573.40

Therefore, the total money you will put into the account is approximately $36,573.40.

c) To calculate the total interest you will earn, subtract the total deposits from the future value:

Total interest = Future value - Total deposits

Total interest = $800,000 - $36,573.40 = $763,426.60

Therefore, the total interest you will earn is approximately $763,426.60.