Question

Year-end contributions of $1000 will be made to a TFSA for 25 years. What will be the future value of the account if it earns 7½% compounded monthly for the first 10 years and 8% compounded semiannually thereafter

Answer 1

Effective compounding rate p.a. for the 1st 10 years = [(1+nominal rate/n)^(n/m)] -1 where

n = number of compoundings in a year; m = number of payments in a year

Effective rate = [(1+7.5%/12)^(12/1)]-1 = 7.76%

Future Value (FV) at the end of 10 years:

PMT (annual payment) = 1,000; rate = 7.76%; N (number of payments) = 10; Type = 0 (as it is end of year payment), solve for FV.

FV = 14,324.71

Effective compounding rate p.a. for the next 15 years = [(1 + 8%/2)^(2/1)]-1 = 8.16%

FV at the end of 25 years:

PMT = 1,000; PV = 14,324.71; rate = 8.16%; N = 15; Type = 0, solve for FV.

FV = 73,953.35 (Answer)