If you wish to accumulate $140,000 in 20 years, how much must you deposit today
ID: 2463258 • Letter: I
Question
If you wish to accumulate $140,000 in 20 years, how much must you deposit today in an account that pays an annual interest rate of 12%? Show work.
If you wish to accumulate $135,000 in 10 years, how much must you deposit today in an account that pays annual interest rate of 14%, with semi-annual compounding of interest? Show Work.
If you deposit $15,500 per year for 9 years in an account that pays an annual interest rate of 10%, what will your account be worth at the end of 9 years? Show Work.
If you deposit $5,000 semi-annually for 5 years in an account that pays an annual interest rate of 10%, what will your account be worth at the end of 5 years? Show Work.
You decide that you need $60,000 in 4.5 years in order to make a down payment on a house. You plan to make semi-annual deposits to achieve your goal. If interest rate is 8%, how much should be deposited each time? Show Work.
You owe $25,000 to your parents for funding some of your college. You promise to make 5 annual payments of $6,750 to settle your debt. Approximately what interest rate are your parents charging, if you make the 5 payments beginning one year from now? Show Work.
You are offered an investment that will pay $24,000 per year for 7 years. If you feel that the appropriate discount rate is 11%, what is the investment worth to you today? Show Work.
You have a rich uncle who has offered you some money upon successfully completing your accounting course. Assuming an annual interest rate of 8%, which alternative should you choose? Show your work for each alternative
$30,000 now
$6,000 a year for 6 years, with the first payment at the end of the first year
$4,000 a year for 5 years with the first payment made at the end of year 1, and then $19,000 at the end of the 6th year.
Explanation / Answer
P = A / (1 + rt)
p = 140000/ (1+(12%*20)=
41,176.47
2-
P = A / (1 + rt)
p = 135000/ (1+(7%*20)= 96428.57
3- fv = ANNUITY AMOUNT*(1+r)n-1+ ANNUITY AMOUNT*(1+r)n-2 +...................ANNUITY AMOUNT*(1+r)n-n
FV = annuity amount * CVAF10% 9 Years
15500*13.579 = 210474.5
4-fv = ANNUITY AMOUNT*(1+r)n-1+ ANNUITY AMOUNT*(1+r)n-2 +...................ANNUITY AMOUNT*(1+r)n-n
FV = annuity amount * CVAF5% Years
5000*12.5778= 62889.46
5- by using the excel function to get the value of semiannually deposits
=PMT(4%,9,0,60000,0)=5669.58
interest rate per semi annual = 8/2 = 4% time period = 4.5*2 = 9 semi annual periods
or FV = annuity amount * CVAF = 60000 = annuity amount * 10.582
Annuity amount = 60000/10.582 = 5669.58
6- rate of interest = r = n[(A/P)1/nt - 1]
5[33750/25000)1/5*4 -1] = 7.79%
7- present value = annuity *PVAF11% 7 Years
24000*4.172 = 100128
4.712196
8- option no 2 Present value = annuity * PVAF = 6000*4.622 = 27732
option no 3 Present value = annuity * PVAF = 4000*3.992 + 19000= 34968
option 1 = 30000
Option 3 is the best one offering 34968
Semiannual period time of compounding compounded value @5% payments future value of payment 1 9 1.55132822 5000 7756.641 2 8 1.47745544 5000 7387.277 3 7 1.40710042 5000 7035.502 4 6 1.34009564 5000 6700.478 5 5 1.27628156 5000 6381.408 6 4 1.21550625 5000 6077.531 7 3 1.157625 5000 5788.125 8 2 1.1025 5000 5512.5 9 1 1.05 5000 5250 10 0 1 5000 5000 compounded value factor 12.5778925 value of deposits 62889.46