Question

1- Suppose you deposit $1000 in an account at the end of each of the next four years. If the account earns 12% annually, how much will be in the account at the end of 7 years?

Answer 1

In the given question, there are 2 components.
1 component is 4 year annuity. 2nd component is keep the annuity maturity
invested in the accounted for next 3 years.
Let's start with the computations
FV of annuity
The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows:
P = PMT x ((((1 + r) ^ n) - 1) / r)
Where:
P = the future value of an annuity stream	To be calculated
PMT = the dollar amount of each annuity payment	$      1,000
r = the effective interest rate (also known as the discount rate)	12%
n = the number of periods in which payments will be made	4
Future value of annuity at year 4	= PMT x ((((1 + r) ^ n) - 1) / r)
Future value of annuity at year 4	= 1000* ((((1 + 12%) ^ 4) - 1) / 12%)
Future value of annuity at year 4	$ 4,779.33
2nd part
This amount at year 4 will be kept invested for next 3 years
The amount at year 7=	Amount * (1+Interest)^time
The amount at year 7=	4779.33 * (1+12%)^3
The amount at year 7=	$ 6,714.61
So amount after 7 years will be $ 6,714.61