help with math problem?

Question

alright. i need some explanation to if you could put it in your answer

You deposit $1000 that has an annual interest rate of 4.5% compounded monthly.
How much money will you have after 5 years if you dont deposit any money.
How much money will you have after 5 years if you deposit $150 every 3 months, after the initial $1000.

Answer 1

Bob's answer ignores compounding.

For the first part, you need to find a future value. The general formula is:

FV = P * (1+R/n)^K

where P is the amount you deposit, R is the annual rate, n is the number of periods per year and K is the total number of periods.
For this problem, the answer is:

FV = 1000*(1+.045/12)^60 = $1,251.80

For the second problem, we need to find the future value of each of the $150 deposits & add it to the 1251.80. You could do this in Excel -- using the formula I give you above.

The other way is to do it in two steps. The first is to notice that the 150 payments form a 20 period annuity. We can find the present value of the annuity using the following formula:

PV = C/r - C/[r*(1+r)^K]

r is the one period return (since this is for three months -- the one period return is (1+4.5%/12)^3-1 = 1.12922%. K is 20 and C is 150.

PV = 2,671.94

But we don't want the PV -- we want the future value -- so we need to multiply it by (1+4.75/12)^60 and add it to the 1251.80

This gives us a total value of $4,596.52


Here is how you can do it in Excel:

First column -- list numbers from 1 to 60.

Second column -- put the values you add (1.000 to start & the 150 every third month after that)

Third column -- put $1000 at the top. Every other cell should have: Previous value times (1+4.5%/12) plus the value in column two.

The bottom cell of column three will have your future value.

If it isn't 4,596.52 -- you did something wrong.

Answer 2

explanation=1000*0.45 interest*60 total months=27000

60/3=20*150=3000 + 27000=30000