Kenny wants to invest $250 every three months at 5.2%/a compounded quarterly. He would like to have at least $6500 at the end of his investment. How long will he need to make a regular payments?

Question

*PLEASE SHOW WORK*

Answer 1

.052/4 = .013 = r
so
multiply by 1.013 every quarter year
n = number of quarter years

Google amount of a sinking fund
S = 250 [(1+r)^n - 1 ] /r
6500 /250 = 26 = [(1+r)^n - 1 ] /r

26 = [ 1.013^n - 1 ]/.013

.338 = 1.013^n - 1
1.338 = 1.013^n
so
n log 1.013 = log 1.338
n (.0056094) = .12646
n = 22.54 quarters
so 5.6 years

Answer 2

for example

http://www.math.utep.edu/Faculty/cmmundy/Math%201320/Worksheets/Sinking%20Funds%20&%20Annuities.pdf