Jan's initial investment is $6000. She is going to deposit $500/mo ($6K/yr) for the next 45 years and get 7% compound interest annually. How is the answer $1,778,831? Can you please provide the formula and how this answer comes to this amount?
1 Answer
This sum can be expressed in the formula:
where
Explanation:
My first assumption was that the interest is paid annually at
Much closer result was with semi-annual payment of interest at 3.5% each half a year, which is equivalent to
Here is the theory.
At year
At year
Do the same up to year
What is the final sum?
Since the initial amount
Additional amount
Continue this process for
This sum can be expressed in the more compact formula using the formula for a sum of geometric progression with factor
For
For
If we assume that the interest is compounded semi-annually (as most bonds do) at the rate
For
The difference between this and your amount might be attributed to rounding during the calculations.