Question

Roland Trin received a graduation present of $20 000 that he is planning on investing in an investment fund, ABC Special Situations Fund, which earns 6% p.a. before fees, compounded every 2 months for a period of 3 years. The fund charges a fee of $100 at the end of each year for management which is subtracted from the fund balance at the time.

In addition to the graduation present, Roland wants to deposit a 6-monthly amount into a high interest cash account with Platinum Securities commencing 1 year from today for 4 payments in total. The account with Platinum Securities has a nominal interest rate of 8% and is compounded half-yearly for a 2-year term. At the end of the investment term there is a fee charged of $150 which is subtracted from the closing account balance.

Roland is looking to buy a car with the total proceeds from the 2 investments with ABC Special Situations Fund and Platinum Securities after 3 years. The car costs $49 000 before additional sales taxes equal to 6% of the purchase price.

Required:

1. How much must Roland deposit each year into Platinum Securities to be successful with his car purchase?
2. What will be the net amount that will come from ABC Special Situations Fund after 3 years to assist with the car purchase?

Group of answer choices

(1) $6 450.14, (2) $28 458.88

(1) $6 708.14, (2) $23 303.11

(1) $6 708.14, (2) $23 604.12

(1) $6 450.14, (2) $23 604.12

(1) $6 416.17, (2) $28 485.88

(1) $6 672.82, (2) $21 233.35

Answer 1

In the given case first we calculate future value of investment of $ 20000 made.

In the given rate interest rate is 6% and it is compounded every two months.

Future Value = Present Value* ((1+ r/(6*100))^n*6)

r= rate of interest

n= no.of years

we take 6 because there is compounding after every two months in a year

As after every year $ 100 are charged as fees, we will calculate future value at the end of every year.

Calculation for year 1

Future Value = 20000*((1+ (6/600))^6)

= 20000* ((1.01)^6)

= 20000 * (1.01)^6

= $ 21230.40

After deduction of $100 value will be $ 21130.40

Now calculation will be for second year

Future Value = 21130.40*((1+ (6/600))^6)

= 21130.40* ((1.01)^6)

= 21130.40 * (1.01)^6

= $ 22430.35

After deduction of $100 value will be $ 22330.35

Now calculation will be for third year

Future Value = 22330.35*((1+ (6/600))^6)

= 22330.35* ((1.01)^6)

= 22330.35 * (1.01)^6

= $ 23704.12

After deduction of $100 value will be $ 23604.12

Total Value of Car Including Tax = 49000*1.06 = $ 51940

We need $ 150 as investment in Platinum Securities at end of year

Net amount required = 51940 + 150 -23604.12

= $ 28485.88

Calculation of 6 monthly deposit to be made

28485.88 = 6 Monthly Deposit * Future Value Factor after Compounding

Calculation of Future Value Compounded Factor

Ist Deposit	(1+(8/200)^(n*4))	(1.04)^4	1.169859
2nd Deposit	(1+(8/200)^(n*3))	(1.04)^3	1.124864
3rd Deposit	(1+(8/200)^(n*2))	(1.04)^2	1.081600
4th Deposit	(1+(8/200)^(n*1))	(1.04)^1	1.040000
			4.416323

In case of Ist Period compounded will be made 4 times because it is for 2 years and compounded is twice and similar calculation for other deposit.

Deposit required every 6 months=28485.88/4.416323

= $6450.14

Answer :(1) $6 450.14, (2) $23 604.12