Lump Sum and Payment Savings 16

Question

If you have $1900 in an account at the start and wish to add $200 to it monthly, how much will you have in 40 years if you assume an 4.25% consistent growth rate that is compounded monthly?

Please note that you will need both the compound interest formula that calculates a "lump sum" balance as well as the savings plan formula for the monthly payment. In other words, your investment can literally be broken down into two parts: the original lump sum $1900 and the continual $200 monthly annuity. They both earn the same APR of 4.25% compounded monthly.

16. Final Balance?

Answer 1

A = p(1 + r/n)^nt + d[((1 + r/n)^nt - 1) / r], Where A = amount, p = principal, r = rate, n = number of calculations per year, d = amount of deposit, t = time in years.

 

A = 1900(1 + 0.0035)^12·40 +200[((1 + 0.0035)^12·40 - 1)) / 0.0425]