Question

Your incredibly wealthy and generous aunt wishes to provide you with a comfortable income over the next four years as you further your studies by completing two degrees. The appropriate interest rate to consider is 5.05% per annum compounded monthly.

a) What amount must your aunt deposit for you now if you are to receive an amount of $1,200 at the end of each month?

b) What amount must your aunt deposit for you now if you are to receive an amount of $1,160 at the beginning of each month?

Answer 1

Solution a:

Monthly rate of interest = 5.05%/12 = 0.42083333%

Periods = 4 years, 48 monthly periods

Let amount to deposited today = X

X = Present value of cash inflows

X = $1,200 * cumulative PV Factor at 0.420833333% for 48 periods for ordinary annuity

= $1,200 * 43.38028 = $52,056

Solution b:

Monthly rate of interest = 5.05%/12 = 0.42083333%

Periods = 4 years, 48 monthly periods

Let amount to deposited today = X

X = Present value of cash inflows

X = $1,160 * cumulative PV Factor at 0.420833333% for 48 periods for annuity due

= $1,160 * 43.56284 = $50,533