Question

Eight months from today you plan to deposit $30,000 into an account with an APR of 4.5% per year with monthly compounding. In addition, ten months from today, you plan to make the first of a series of quarterly deposits into the same account. Your first deposit will equal $2000 and subsequent deposits will grow by 1.5% each. You will make your final deposit four years and one month from today. How much will be in your account five years from today if you make no withdrawals before then?

Answer 1

Given :
Interest rate =APR 4.5% ps with monthly compounding=	0.375% per month
EAR =(1+4.5%/12)^12-1=4.5940% pa
Effective interest /Qtr =4.5940/4=1.148% per qtr.
There will be two parts in the Matrutiy value calculation
Part 1.
$30,000 deposited in 8 months from now will be
compounded for 53 months till matuity after 5 years.
Maturity Value =30000*(1.00375)^53=	$                36,582.71
Part 2.
There will be a growing annuity of 14 qtrs
We shall find the maturity value after 47 yrs 1 month
Future Value of Growing Annuity =
C/(r-g) *[1-(1+g)^n/((1+r)^n]*(1+r)^n
C = Periodic payment=$2000
i = Discount rate=
g = Growth rate
n = Number of periods
FV=2000/(1.148%-1.5%)*[1-(1.015/1.0148)^14]*1.0148^14
FV =$33224.03
So FV of the annuity after 4 years 1 months =	$                33,224.03
So FV of the annuity after 5 years=33224.03*(1+0.375%)^11=	$                34,620.51
The the total amount available after 5 yrs=$36,582.71+$34,620.51=	71,203.22