Thread: financial mathematics

a family wishes to accumulate $50000 in a college education fund att rhe end of 20 years. If they deposit $1000 in the fund at the end of each of the first 10 years and $1000+X in the fund at the end of each of the second 10 years, find X to the nearest dollar if fund earns an effective interest annual rate of 7%

Do it in 3 steps:

1: $1000 deposited for 10 years at 7% annually = 13,816.45

2: $13,816.45 @ 7% annually for 10 years (11 to 20) = 27,179.04

So the amount that the new annual deposit of 1000+x must accumulate
to over 10 years (11 to 20) is 50,000 - 27,179.04 = 22,820.96

3: Annual deposit for 10 years (11 to 20) at 7% annually that
accumulates to 22,820.96 = 1,651.72 ; so x = 651.72

This can be easily done by using financial formulas; as example:
(1000 + x)(1.07^10 - 1) / .07 = 22820.96
Solve for x: 651.72

Now YOU do some work: find the formulas