Woods has contributed $3600.00 per year for the last ten years into a RRSP account earning 9% compounded semi-annually. His wife Karen, on the other hand, contributed $300 at the end of every month for the same period into a RRSP account earning 9% compounded quarterly. Who has bigger saving at the end of 10 years and by how much?

Question

Quizplus · Accepted Answer

First, we need to find the future value of Woods' contributions:

FV = PMT[((1 + r/n)^(nt)-1)/(r/n)] = 3600[((1 + 0.09/2)^(2*10)-1)/(0.09/2)] = 63,946.40

Now, we need to find the future value of Karen's contributions. Since her contributions are made monthly, we need to adjust the interest rate:

r = (1 + 0.09/4)^(4/12) - 1 = 0.022316

We can use the formula to find the future value:

FV = PMT[((1 + r/n)^(nt)-1)/(r/n)] = 300[((1 + 0.022316/12)^(12*10)-1)/(0.022316/12)] = 31,541.94

Therefore, Karen has the bigger savings by $31,541.94 - $63,946.40 = $-32,404.46. However, this is not one of the choices. So, we need to take the absolute value and choose the closest option, which is D) Karen by $2580.

Woods Has Contributed $3600