Question

You plan to save money for a down payment of $44,000 to purchase an apartment. You can only afford to save $6,000 at the end of every 6 months into an account that earns interest at 5.50% compounded monthly. How long will it take you to save the planned amount?

years

months

Answer 1

Monthly rate = 5.50%/12 =0.45833333%
Six monthly effective rate = (1+0.00458333333)^6 - 1
=2.7817036%
Calcuation of period it will take
Future Value of an Ordinary Annuity
= C*[(1+i)^n-1]/i
Where,
C= Cash Flow per period
i = interest rate per period=2.7817036%
n=number of period
$44000= $6000[ (1+0.027817036)^n -1] /0.027817036
44000= $6000[ (1.027817036)^n -1] /0.027817036
n=6.7661 six months period
that menas = 6.7661/2 =3.38305 years
that mens = 3 years +0.38305*12
=3 years 4.60 months or 3 years & 5 months