5a Congratulations youve just purchased your first home for

5a. Congratulations, you’ve just purchased your first home for $360,000! Your 30 year mortgage is $300,000. Your annual mortgage payments are $24,000. What interest rate is the bank charging you?

5b.If instead you had the choice of making monthly payments of $2,000 for 30 years, what would the interest rate be?

6a.   Assume that you are now 30 years old. You would like to retire at age 65 and have a retirement fund of $1,000,000. You already have $10,000 at age 30 in retirement savings (401K,IRA). You expect to earn 5% per year. The amount of money you must set aside each month to reach your retirement goal is:

6b. At 65, if the appropriate discount rate is 7%, what amount can you get as an annuity for the next 25 years if you want to exhaust your savings by your death at 90?

Solution

(5a)

Present Value = Annuity x Present Value Interest Factor of Annuity (r%, 30 years)

$300,000 = $24,000 x Present Value Interest Factor of Annuity (r%, 30 years)

Present Value Interest Factor of Annuity (r%, 30 years) = 12.5

From PVIFA table, the value closest to 12.5 is 12.4 when N = 30 & r = 6%

So, interest rate is 6.%

(5b)

Using financial calculator:

Annuity = 2000 [PMT]

N = number of periods = 30 x 12 = 360

PV = 300,000

I/Y = 0.585 (Per month) = 7.02% per year

(6a)

FV of $10,000 after 35 years = $10,000 x (1.05)³⁵ = $55,160

Money required after 35 years = $(1,000,000 - 55,160) = $944,840

Using financial calculator,

FV = 944,840

N = 35 x 12 = 420

I = 5% per year = 0.42% per month

PMT = $824.29 (savings per month)

NOTE: Out of 4 questions the first 3 are answered.