Question

The insurance company which manages the retirement fund promises to pay a stated (or nominal) rate of 12% per year, but with quarterly compounding. if your mother invests $1000 each six months, starting 18 months from today, how much will she have 5 years from now, assuming the last payment is made at the end of year 5?

Draw the time lines for all the problems and show all the formulas/equations.

Answer 1

Time Period	Investment value	Interst rate multiplier	Calculation of multiplier	Amount
0	$ -
6	$ -
12	$ -
18	$ 1,000.00	11.9764	(1.03), 84 times	$ 11,976.42
24	$ 1,000.00	8.4000	(1.03), 72 times	$    8,400.02
30	$ 1,000.00	5.8916	(1.03), 60 times	$    5,891.60
36	$ 1,000.00	4.1323	(1.03), 48 times	$    4,132.25
42	$ 1,000.00	2.8983	(1.03), 36 times	$    2,898.28
48	$ 1,000.00	2.0328	(1.03), 24 times	$    2,032.79
54	$ 1,000.00	1.4258	(1.03), 12 times	$    1,425.76
60	$ 1,000.00	1.0000	(1.03), 0 times	$    1,000.00
				$ 37,757.12

The given rate of interest is 12% , which is compounded quarterly. Then interest rate each quarter will be 3%

Formula using the problem is so just Instalment value * Interest rate multiplier which is compunded quarterly

For Ex. first installment paid on 18 months so the period for which interest compounded is 84 quarters.