1.) Time to reach a financial goal You have $44,524.78 in a brokerage account, a

Question

1.) Time to reach a financial goal

You have $44,524.78 in a brokerage account, and you plan to deposit an additional $4,000 at the end of every future year until your account totals $270,000. You expect to earn 12% annually on the account. How many years will it take to reach your goal? Round your answer to two decimal places at the end of the calculations.

2.) Future value: annuity versus annuity due

a.)What's the future value of a 11%, 5-year ordinary annuity that pays $800 each year? Round your answer to the nearest cent.

$  

b.) If this was an annuity due, what would its future value be? Round your answer to the nearest cent.

$  

3.) Present and future values of a cash flow stream

An investment will pay $50 at the end of each of the next 3 years, $250 at the end of Year 4, $350 at the end of Year 5, and $600 at the end of Year 6.

a.) If other investments of equal risk earn 8% annually, what is its present value? Round your answer to the nearest cent.

b.) If other investments of equal risk earn 8% annually, what is its future value? Round your answer to the nearest cent.

4.) Loan amortization and EAR

You want to buy a car, and a local bank will lend you $30,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 7% with interest paid monthly.

What will be the monthly loan payment? Round your answer to the nearest cent.

$  

What will be the loan's EAR? Round your answer to two decimal places.

%

5.) Growth rates

Shalit Corporation's 2011 sales were $6 million. Its 2006 sales were $3 million.

At what rate have sales been growing? Round your answer to two decimal places.

%

6.) Effective rate of interest

Find the interest rates earned on each of the following. Round each answer to two decimal places.

You borrow $650 and promise to pay back $715 at the end of 1 year.

%

You lend $650 and the borrower promises to pay you $715 at the end of 1 year.

%

You borrow $70,000 and promise to pay back $648,587 at the end of 15 years.

%

You borrow $11,000 and promise to make payments of $3,359.50 at the end of each year for 5 years.

%

Explanation / Answer

1) Amount required = 270,000 - 44524.78 = 225,475.2

So

225,475.2 = annual fixed payment x [(1 + r)n - 1] / r = annual fixed payment x FV Annuity Factor (r, n)

= 4000 x FVAF (r, n)

So FVAF (12, n) = 225475.2 / 4000 = 56.3688

When n = 18 years, this value is closest to corresponding FVAF = 55.7497

So n = 18 yrs

2)

2 - a)

FV = annual fixed payment x FV Annuity Factor (r, n)

= 800 x FVAF (11%, 5) = 800 x 6.2278 = 4982.24

2 - b)

If it were Annuity Due,

FV = annual fixed payment x FV Annuity Factor (r, n) x (1 + r)

= 4982.24 x 1.11 = 5530.29

3)

3 - a) PV = 50 x PVIFA (8%, 3) + 250 x PVIF (8%, 4) + 350 x PVIF (8%, 5) + 600 x PVIF (8%, 6)

= 50 x 2.5771 + 250 x 0.7350 + 350 x 0.6806 + 600 x 0.6302

= 128.85 + 183.75 + 238.21 + 378.12 = 928.93

3 - b)

If PV = 928.93 then FV = 928.93 x (1.08)6 = 1474.09

(5) ratio of sales (2001 and 2006) = 6 / 3 = 2

If growth rate = x% in 5 years, then x = approx 14.5% (from FV Factor table)

(6)

6 - a)

Interest paid = 715 - 650 = 65

So interest % = 65 / 650 = 10.00%

6 - b)

Interest I received = 715 - 650

so interest % = 65 / 650 = 10.00%

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