Ethan converted his RRSP into a RRIF that pays him $1,500 at the beginning of every month for three years followed by $2,000 at the beginning of every month for the next five years. If the rate of return of the annuity is 3.85% compounded monthly during the entire period, what was the value of RRIF?
To find the value of the Registered Retirement Income Fund (RRIF), we can calculate the present value of all the monthly payments using the formula for the present value of an annuity.
The formula for the present value of an annuity is:
PV = Pmt * (1 - (1 + r)^(-n)) / r
Where:
PV is the present value of the annuity
Pmt is the monthly payment
r is the interest rate per period (compounded monthly)
n is the total number of periods
Let's break down the given information and calculate the present value of each payment separately.
1. For the first three years:
Monthly payment = $1,500
Interest rate per period (compounded monthly) = 3.85% / 12 = 0.3208%
Number of periods = 3 * 12 = 36
PV1 = 1,500 * (1 - (1 + 0.003208)^(-36)) / 0.003208
2. For the next five years:
Monthly payment = $2,000
Interest rate per period (compounded monthly) = 3.85% / 12 = 0.3208%
Number of periods = 5 * 12 = 60
PV2 = 2,000 * (1 - (1 + 0.003208)^(-60)) / 0.003208
Now, we can calculate the total present value of the RRIF by summing the two present values:
Total Present Value = PV1 + PV2
After calculating the above expression, we will get the value of the RRIF.