Question

Assume the appropriate discount rate is 9%. What is the value 11 years from today of an annuity that makes payments of $6,000 per year if the first payment is made 12 years from now and the last payment is made 20 years from now?

Today, you open a new savings account and plan to begin depositing equal amounts at the beginning of each year for 6 years, including the deposit you make today. There will only be these 6 deposits and no withdrawals. Assume the interest rate you will earn is 7%. If you want your account balance to be exactly $35,000 at the end of 6 years, what must be the amount of each deposit?

At an annual interest rate of 8%, how many years does it take to quadruple your money?

Answer 1

1) To find the value 11 years from today of money startting deposits 12 years from today , simply but looking for a present value of today which is depostitng equal paymrnts per year for next 8 years. (Scale down)

therefor PV=cash flow/(1+r) + cashflow/(1+r)^2......+ cashflow/(1+r)^8 , cash flow per year = 6000, rate =9%

that is present value = 6000/(1+.09) + 6000/(1+.09)^2 + 6000/(1+.09)^3 + 6000/(1+.09)^4 + 6000/(1+.09)^5 + 6000/(1+.09)^6 + 6000/(1+.09)^7 + 6000/(1.09)^8

= 5504.5 + 5050.07 + 4633.1 +4250.55 + 3899.58 + 3577.6 + 3282.20 + 3011.19

Value 11 years from now = $33208.9 = $33209

at an annual interest of 8% , quadruple = 4 times.

future value = present value * (1 + r)^t , fv=4pv ,r =8%

4pv=pv(1+.08)^t, 4=1.08^t ,

Solving for T gives = 18 Years.

c)   Future Value = $35000 , T = 6 years , Rate = 7%

USING EXCEL FORMULA = PMT(RATE,NPER,PV,FV,TYPE) = PMT(8%,6,0,35000,1) = $4417.63

EVERY YEAR HAS TO MAKE $4417.63