Question

Jane invests 500 at t=0 at a nominal annual interest rate of 6%, compounded
quarterly. What additional amount will she need to invest at t=2 in order to have a total of 1,000 at t=5?

Answer 1

500(1.015)^20 + x(1.015)^16 = 1000
1.268985... = 326.572..
x = $257.35

Answer 2

I miscounted on my "time line"

should have been:

500(1.015)^20 + x(1.015)^12 = 1000
...
x = $273.14

Answer 3

amount at end of t = 2
= 500(1.015)^8
= 563.25
add additional payment of 273.14
= 836.39

amount of that after 3 more years
= 836.39(1.015)^12
=999.9986..
not bad, eh?