The 6.2% account:
Good nuff?Code:YR DEPOSIT INTEREST BALANCE 1 56.00 .00 56.00 2 112.00 3.47 168.47 ... 10 560.00 185.09 3730.4829.....
A man invests 1000 at the beginning of each year into a fund that pays an annual interest rate of 5.6%. The annual interest payments are deposited into a fund that pays 6.2% annually. What is his total accumulation at the end of 10 years?
I thought that the way to solve this problem was:
But the answer in the back of my book says that the the annuity is increasing, but I don't understand how.
The amount of interest for year k is 1000k(0.056)=56k. The accumulation of these payments plus interest is 56(Is)_{10,0.06}=3,730.48. Total accumulation is 13,730.48.
Can someone explain how that answer was achieved? Thanks.
u = 1st payment (56)
v = constant payment increase (56)
n = number of periods (10)
i = interest rate per period (.062)
r = 1 + i (1.062)
f = future value (?)
f = { i [u(r^n - 1) - v(n - 1)] + vr[r^(n - 1) - 1]} / i^2
f = 3730.4829.....
Above also handles problems like:
Jack opens annuity account in which he deposits $500 as 1st annual payment,
then increases payments by $50 each year....u = 500, v = 50