Question

Module #6 Hand - In Assignment 1. An article on saving for retirement estimates that a 35 year old will need 1.2 million to retire at age 65. a. How much money should you deposit today to reach that goal if your investments will return 8% compounded semi-annually. b. You currently have only $80,000 in your retirement savings plan what semi-annual rate of return do you need to reach your retirement goal? (assume same return as a) c. You estimate you can achieve an annual rate of return of 10% effective. How old will you be when you retire if you have $80,000 now? 2. Premium Canada savings bonds have the following rates (all effective) Year 1 2.45% Year 2 2.8% Year 3 3% Year 4 3.5% Year 5 5% a. How much would a $1000.00 investment be worth at the end of the fifth year? h What suarase effective rate was earned?

Answer 1

A. Calculation of amount to be invested today :

Given:

Future Value= $12,00,000

Rate of Return= 8% Compounded Semi-Annually

Time = 30 years

Formula :

Future Value = Present Value * ( 1 + (rate/2))time*2

$12,00,000 = Present Value * (1+(0.08/2))30*2

$12,00,000 = Present Value * 10.5196

It implies

Present Value = $12,00,000/10.5196

Present Value = $1,14,072

Hence, amount required to be invested now to get $1.2 million after 30 years at the rate of 8% compounded semi-annually is $1,14,072.

B. Calculation of Semi-Annual rate of return :

$12,00,000 = $80,000 * (1+(rate/2))30*2

$12,00,000/$80,000 = (1+(rate/2))60

60th root of 15 = (1+(rate/2))

1.0462 = 1+(rate/2)

1.0462 = (2+rate)/2

1.0462 * 2 = 2+rate

2.0924 = 2+rate

It imples

rate = 2.0924 -2

Therefore,

rate- .0924 i.e., 9.24%

C. Calculation of age :

Effective rate of return annually = 10%

$12,00,000 = $80,000 * (1+rate)time

15 = (1+0.10)time

15 = (1.10)time

Using logarithm :

log1.1015 = x

Using change of base rule of log:

log15/log1.10 = x

Therefore, after solving

x=28.413 years