Question

1.         In order to accumulate enough money for a down payment on a​ house, a couple deposits $745 per month into an account paying 6% compounded monthly. If payments are made at the end of each​ period, how much money will be in the account in 6 years?

2.         Find the payment that should be used for the annuity due whose future value is given. Assume that the compounding period is the same as the payment period.

$14,000​; quarterly payments for 13 years; interest rate 7.5​%.

The payment should be _______

​

3.         Find the future value for the annuity due with the given rate.

Payments of $180 for 4 years at 0.31​% compounded quarterly

The future value of the annuity due is _______

4.         Find the future value for the annuity due with the given rate.

Payments of $17,000 for 12 years at 0.24​% compounded monthly

The future value of the annuity due is ________

​

5.         Find the interest rate needed for the sinking fund to reach the required amount. Assume that the compounding period is the same as the payment period.

​$30,275 to be accumulated in 5 years; quarterly payments of $1300.

The interest rate needed is approximately _______%

Answer 1

1)	Value in 6 years	=	Annuity	x	Future value of annuity of 1
		=	$             745	x	86.40886
		=	$ 64,374.60
	Working:
	Future value of annuity of 1	=	(((1+i)^n)-1)/i			Where,
		=	(((1+0.005)^72)-1)/0.005			i		6%/12	=	0.005
		=	86.4088557			n		6*12	=	72