Question

a) A contract requires that Bob makes payments of $1319 and $3728 to Jim 24 and 45 months respectively. Bob would like to change the payment structure to a payment of $1901 today, and a second payment made 45 months from today. If the two sets of payments are economically equivalent, and the interest rate is 6% compounded quarterly, then what is the amount of the second payment? Give your answer rounded to the nearest cent.

b) Ellenor pays month-end payments of $843 into her RRSP for 33 years. The RRSP has an interest rate of 4% compounded quarterly. At the end of 33 years, she purchases an annuity that will pay her bi-weekly payments (at the end of each bi-weekly period) for 32 years. The interest of the annuity is 3% compounded semi-annually. How much are Ellenor's biweekly payments when she retires?

Answer 1

1.
1319/(1+6%/4)^8+3728/(1+6%/4)^15=1901+x/(1+6%/4)^15
=>x=$2,815.19

2.
rate compounded monthly=((1+4%/4)^(4/12)-1)*12
Accumulated value=843/(((1+4%/4)^(4/12)-1)*12/12)*((1+((1+4%/4)^(4/12)-1)*12/12)^(12*33)-1)=$689,911.63

rate compounded biweekly=((1+3%/2)^(2/26)-1)*26
Biweekly payments=689911.63*(((1+3%/2)^(2/26)-1)*26/26)/(1-1/(1+((1+3%/2)^(2/26)-1)*26/26)^(26*32))=$1,286.84