Sigrid contributed $200 every month for nine years into an RRSP earning 4.3% compounded annually. She then converted the RRSP into an annuity that pays her monthly for 20 years. If the first payment is due one month after the conversion, and interest on the annuity is 5.4% compounded semi-annually, how much will Sigrid receive at the end of every month?

Question

Sigrid contributed $200 every month for nine years into an RRSP earning 4.3% compounded annually. She then converted the RRSP into an annuity that pays her monthly for 20 years. If the first payment is due one month after the conversion, and interest on the annuity is 5.4% compounded semi-annually, how much will Sigrid receive at the end of every month?

Answer 1

Any idea how to get started on this? Where are you getting stuck?

Answer 2

the future value of the RRSP is

(200*12)((1+.043)^9-1)/(1.043-1) = 25713.07
Note that since the interest is only compounded annually, you just work with a single yearly contribution.
If it were compounded monthly, it'd be 200((1+.043/12)^(12*9)-1)/(1.043-1)

Now just drag out your formula for annuity amortization...

Answer 3

To calculate the amount Sigrid will receive at the end of every month after converting her RRSP into an annuity, we first need to determine the future value of her contributions.

1. Calculate the future value of Sigrid's monthly contributions for nine years in the RRSP. We can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^(n*t) - 1] / r

FV = Future Value
P = Monthly payment
r = Annual interest rate (compounded annually)
n = Number of compounding periods per year
t = Number of years

Plugging in the values:
P = $200
r = 4.3% = 0.043 (as a decimal)
n = 1 (compounded annually)
t = 9 years

FV = $200 * [(1 + 0.043)^(1*9) - 1] / 0.043
FV ≈ $22,708.95

2. After converting the RRSP into an annuity, Sigrid will receive monthly payments for 20 years. We will use the formula for the present value of an ordinary annuity:

PV = C * [1 - (1 + r)^(-n)] / r

PV = Present Value (the amount Sigrid will receive at the end of each month)
C = Monthly payment
r = Annual interest rate (compounded semi-annually)
n = Number of compounding periods per year * Number of years

Plugging in the values:
C = ?
r = 5.4% / 2 = 0.054 / 2 = 0.027 (as a decimal)
n = 2 (compounded semi-annually) * 20 years = 40

We need to find the value of C, which is the monthly payment Sigrid will receive. Rearranging the formula:

C = PV * r / [1 - (1 + r)^(-n)]

Plugging in the values:
PV = $22,708.95 (future value of RRSP)
r = 0.027
n = 40

C = $22,708.95 * 0.027 / [1 - (1 + 0.027)^(-40)]
C ≈ $157.53

Therefore, Sigrid will receive approximately $157.53 at the end of each month after converting her RRSP into an annuity.

Any idea how to get started on this? Where are you getting stuck?

the future value of the RRSP is

380.67

To calculate the amount Sigrid will receive at the end of every month after converting her RRSP into an annuity, we first need to determine the future value of her contributions.