1) You have decided to put a $100 a week into a savings account that offers 2.6%
ID: 2774489 • Letter: 1
Question
1) You have decided to put a $100 a week into a savings account that offers 2.6% compounded weekly. How much would you have in your account after 6 years? Answer: _________________________ 2) Using problem 2 how much would you have if you were to make your first payment today, i.e. made it into an annuity due problem? Answer: _________________________
3) Your child was born today and you have decided to put money into his education fund starting today (annuity due). Your account earns 4.5% compounded monthly. If you want there to be $200,000 for him in the account on his 18th birthday how much do you have to contribute every month? Answer: _________________________
4) What is the combined present value of $5,000 to be received in 5 years, $15,000 to be received in 10 years, and $25,000 to be received in 15 years with an interest rate of 9.0%? Answer: _________________________
5) Your parents have decided they want to put money away today so that beginning on your 45 th birthday that you get $10,000 for 35 years. Today you turned 21. If your parents account guarantees 8.80%, how much money do they need to put in the account today? Answer: _________________________
6) What is the present value of a perpetuity that pays $2,500 a year, if we expect interest rates to be 12.75% forever? Answer: _________________________
7) You have decided to open up a savings account. Your bank has offered you three interest options: A) 10.55% annually, B) 10.40% quarterly and C) 10.30% weekly. Which do you prefer? Answer: _________________________ Justify your answer: __________________________________________________________ ___________________________________________________________________________
8) What is the present value of $1,000 a month to be received for the next 50 years with an interest rate of 8.0% compounded monthly? Answer: _________________________
9) What is the present value of $12,000 a year to be received for the next 50 years with an interest rate of 8.0%? Answer: _________________________
10) You just won the Powerball, as a result you have the choice between taking $250 million today or taking a 20-year annuity. Interest rates are expected to hold at 3.75% over the next 20-years. How much would the annuity need to be annually for you to be indifferent between cash now or taking the annuity? Answer: _________________________
11) (Bonus Question – 5 points) What is the present value of $25,000 received in 10 years if interest rates are 6.5% with continuous compounding? Answer: _________________________
Explanation / Answer
1)
Future value of annuity = P×[(1+r)^n-1]÷r
r is interest rate
P is payment per period
n is number of payments
= $100×[(1+(2.6%÷52))^(6×52)-1]÷(2.6%÷52)
= $33,756
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