If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?

Question

How much should you invest each month in order to have $800,000 if your rate of return is 5.3% compounded monthly and you want to achieve your goal in 40 years?

 

If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?

Answer 1

1. INPUTS
1. FV (Future Value) = $800,000
2. T (time) = 40 years
3. I (interest rate) = 5.3% compounded monthly
2. OUTPUTS
1. Let's put everything in terms of months
2. P (time periods) = 40years * 12 months/ year = 480 months
3. I (monthly interest rate) = 5.3% /12 = 0.44167%
4. Now, it depends how you want to go about solving this problem.  I used the financial function capabilities of Excel.  Use the function PMT, which requires you to enter (rate, nper, pv, [fv], [type]).  The rate is simply 0.44167%, the nper is 480, the pv (present value) is 0, the fv is 800,000 and the type is 0.  The type simply is a way to say whether the payment occurs at the beginning of the month or at the end of the month.  A zero value is the end of the period/month.  Note that in the problem description, it is not clear when the payment is made.  Also note that PMT = payment = the amount you invest each month.
5. When =PMT(0.44617%, 480, 0, 800000, 0) is entered into Excel, it returns $484.53.  This is the amount you should invest each month.
3. If you want to achieve your goal (800000) in 20 years, then (again using the PMT function in Excel), you need to invest $1879.79.
4. So now you are investing $1879.79 each month.  This is your payment.  And the problem asks how much you will have (future value) in 10 years (120 months), with an interest rate of 0.44167%/mo.  
5. Now use the Excel function FV.  The format of the FV function is FV(rate, nper, pmt, pv, type).  Plugging in the values results in =FV(0.44167%, 120, 1879.79, 0, 1).  The result is $297,941.99.  This is what your savings will be worth after 10 years