Question

Question:

You recently received a bonus of $8,000 and are thinking of investing this sum of money for your retirement 20 years later. Sandy Chen, your financial planner, approached you recently an offered two investment products. Product Aee will earn an annual return of 5% per year for the first 5 years. If there is no recession in Singapore during the first 5 years, all amounts invested will earn an annual return of 7% for the next 10 years, otherwise, returns will be 3% per year. Alternatively, Product Bee allows you to invest $800 per year (at the beginning of each year) for the next 10 years. It will earn a return of 5% per year. This product will mature 20 years later. Over the next two decades, the deposit rate offered by local banks is expected to be 2% per year, which is compounded daily. Whereas, lending rates are expected to be 6% per year (compounded monthly). Based on a recent article you read from Business Times, economists have predicted that there will be a 70% chance of a recession happening over the next several years.

(a) Calculate the amount you expect to receive at the end of 15 years for Product Aee if there is no recession during the first 5 years.

(b) Calculate the amount you expect to receive at the end of 15 years for Product Aee if there is a recession during the first 5 years.

(c) Calculate the value of Product Bee on maturity. (4 marks) (d) Calculate the effective interest rate of both deposit and lending rates.

(d) Calculate the effective interest rate of both deposit and lending rates.

(e) Determine and justify which investment product you should choose. State any assumptions made.

Answer 1

(a)

Amount to be received after 15 years for Aee if there is no recession during first 5 years

For first 5 years

Pv

Deposit in the beginning

$8,000

Rate

Interest rate

5%

Nper

Number of years

5

FV

Amount accumulated at end of 5 years

$10,210.25

(using excel FV function with Rate=5%, Nper=5, Pv=-8000)

Next 10 years

Pv

Amount available in the beginning

$10,210.25

Rate

Interest rate if there was no recession

7%

Nper

Number of years

10

FV

Amount accumulated at end of 15 years

$20,085.11

(using excel FV function with Rate=7%, Nper=10, Pv=-10210.25)

(b)

Amount to be received after 15 years for Aee if there is recession during first 5 years

Next 10 years

Pv

Amount available in the beginning

$10,210.25

Rate

Interest rate if there was recession

3%

Nper

Number of years

10

FV

Amount accumulated at end of 15 years

$13,721.73

(using excel FV function with Rate=3%, Nper=10, Pv=-10210.25)

.(c)

Value of product Bee on maturity

Pmt

Amount invested per year

$800

Rate

Interest Rate

5%

Nper

Number of years

10

FV

Amount accumulated at end of 10 years

$10,565.43

(using excel FV function with Rate=5%, Nper=10, Pmt=-800,Type=1(Beginning of year deposit)

Next 20years:

Interest rate =2% compounded daily

Rate

Annual effective rate=((1+(0.02/365))^365)-1

0.02020078

PV

Amount available in the beginning of 20 year period

$10,565.43

Nper

Number of years

20

Fv

Value of product Bee on maturity

$15,761.60

(using excel FV function with Rate=0.02020078, Nper=20,Pv=-10565.43)

Effective deposit Rate

0.02020078

Effective deposit Rate(Percentage)

2.020078%

Lending rate 6% compounded Monthly

Effective Lending rate=((1+(0.06/12))^12)-1=

0.06167781

Effective Lending rate(Percentage)=

6.17%

Product Aee Amount on Maturit Probability $20,085.11 $13,721.73 0.3 (No recession) 0.7 (Recession Expected amount after 15 years 20085.11*0.3+13721*0.7 $15,630.74 Expected annual return ((15630.74/80000)A(1/15))-1 Expected annual return= 0.045665 1.95 1.045665163 0.045665 45710 Product Bee Cash Flow Year 0 ($800) ($800 ($800 ($800 4 ($800) ($800 6 ($800) ($800 8 ($800) ($800 S0 S0 10 12 13 14 15 16 17 18 19 20 21 23 24 25 26 27 28 29 30 $15,761.60 Effecti ve Annual Return(Using IRR function of excel) Over the Cash Flow Product Aee should be chosen Expeceted returnis 2.68% higher than product Bee