Question

1) You have an investment account that started with $3,000 10 years ago and which now has grown to ​$11,000.

a. What annual rate of return have you earned​ (you have made no additional contributions to the​ account)?

b. If the savings bond earns 16% per year from now​ on, what will the​ account's value be 10 years from​ now?

2) You are thinking of purchasing a house. The house costs $250,000. You have $36,000 in cash that you can use as a down payment on the​ house, but you need to borrow the rest of the purchase price.

The bank is offering a 30​-year mortgage that requires annual payments and has an interest rate of 6% per year. What will be your annual payment if you sign this mortgage?

Answer 1

1.a.We use the formula:  
A=P(1+r/100)^n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

11000=3000*(1+r/100)^10

(11000/3000)^(1/10)=(1+r/100)

(1+r/100)=1.1387

r=1.1387-1

=13.87%(Approx)

b.A=11000*(1.16)^10

=11000*4.41143508

=$48525.79(Approx)

2.Borrowings=(250,000-36000)=$214,000

Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

214,000=Annuity[1-(1.06)^-30]/0.06

214,000=Annuity*13.7648312

Annuity=214,000/13.7648312

=$15546.87(Approx)