Question

1.Portfolio Investment.

An investor has decided to invest $13,000 in an S&P 500 index fund and $7,000 in 10-year treasury bonds (T-bonds). The index fund is expected to have an average annual rate of return of 6.8%. The T-bonds are guaranteed to pay annual interest of 0.70% (as of Oct 2, 2020).

Assuming the stock market return is as the investor expects, how much will this $20,000 investment be worth the end of 10 years?

2.Refer to the Portfolio Investment assumptions above. What is the compound annual growth rate of her portfolio over the 10 years?

Car Savings Scenario

A couple receives bonuses each year from their jobs. They are planning to invest $10,000 of the bonuses each year, starting today, to buy a new car in 5 years. Assume their investments have a 4% annual rate of return.

3.If their investments return 4.0% a year and they start today, how much will they have at the end of 5 years?

4.Assume the same scenario as above. What is the Present Value of the car fund investments above over 5 years? Remember, the first annual investment occurs today.

5.What is the Present Value of the car fund investments above over 5 years, if the first annual investment is a year from now?

Retirement Savings Scenario

A business professional lands a new job that pays $120,000 a year. He plans to invest 11% of his salary in a 401K. His employer will match 3% of his salary. He will rollover $145,000 from his last employer's 401K into the new 401K

6.How long would it take the 401K to reach $1,000,000, if the compound average annual rate of return is 8.2% a year? (Be sure to include his contribution, his employer’s contribution, and his 401K rollover. Assume the contributions are made once a year, starting a year from now.)

7.How much will the 401K be worth in 25 years? (Use the same assumptions as the problem above.)

8.How long would it take to double the value of an investment, if its value grows 4.75% a year?

Answer 1

Future value of investment in index fund	present value*(1+r)^n	13000*1.068^10	25098.96883
Future value of investment in treasury bond	present value*(1+r)^n	7000*1.007^10	7505.726679
1-Total future value of portfolio Investment			32604.70
2-Compound annual growth rate	(future value of portfolio/Initial Investment in portfolio)^(1/n)-1	(32604.7/20000)^(1/10)-1	5.01%
3-how much will they have at the end of 5 years =Using future value function in MS excel	FV(rate,nper,pmt,pv,type) rate =4% nper =5 pmt =-10000 pv =0 type =1	FV(4%,5,-10000,0,1)	$56,329.75
4-Present Value of the car fund investments above over 5 years =Using present value function in MS excel	pV(rate,nper,pmt,fv,type) rate =4% nper =5 pmt =-10000 fv =0 type =1	PV(4%,5,-10000,0,1)	$46,298.95
5-Present Value of the car fund investments above over 5 years, if the first annual investment is a year from now?	pV(rate,nper,pmt,fv,type) rate =4% nper =5 pmt =-10000 fv =0 type =0	PV(4%,5,-10000,0,0)	$44,518.22