If your credit card\'s APR is 24% compounded daily, what is the effective annual
ID: 2564707 • Letter: I
Question
If your credit card's APR is 24% compounded daily, what is the effective annual interest rate that you are paying? 2. You want to accumulate $500,000 in a savings account in 20 years. If the bank pays 6% compounded annually, how much should you deposit in the account? . What is the future value 8 years from, of S 2,000 invested today at a periodic interest rate of 12% compounded annually? What would be the result of the previous problem, if simple interest were used? s. Carrie Mathison plans to retire in 30 years. She intends to contribute the same amount of money each year to her retirement fund. The fund earns 10% compounded annually. She would like to withdraw $100,000 each year for 20 years, starting one year after the last contribution is made. each year? How much money should she contribute to her fund 6. A new rail car costs S100,000 and is expected to last for twenty years, assuming that $20,000 is spent on a major overhaul at the end of year 10. Routine servicing and maintenance are expected to cost $2,000 per year. The car is expected to be used in revenue service for 300 days per r. What is the equialentcost per-day -in-use over the year twenty-year life of the car, assuming a discount rate of 10%? 7. An industrial firm uses an economic analysis to determine which of two different machines to purchase. Each machine is capable of performing the same task in a given amount of time. Assume the minimum attractive rate of return is 8%. Use the following data in this analysis. Initial cost Estimated life Salvage valuc Annual maintenance cost S150 Machine x Machine y $6000 $12.000 7 years 13 years none $4000 $175 Which, if either of the two machines should the firm choose based on equivalent uniform annual costs?Explanation / Answer
1) Interest Rate per day = 24%/365 = 0.066% (Assuming 1 year = 365 days)
no. of interest periods per year = 365
Effective Annual Interest rate :
ia = (1+r/M)M - 1 = (1+0.066%)365 - 1 = 27.1149%
Where, ia = effective annual interest rate
M = number of interest periods per year
r = nominal interest rate per year (APR)
(I have used Effective interest rate calculator for this calculation as it is very complicated to calculate without that)
2) Total Savings = Deposit * (1+r)n
Where, r = rate of interest, n = no. of terms of compounding
$500,000 = Deposit * (1+0.06)20
Deposit = $500,000/3.2071 = $155,904
3)Future Value = Amount invested* FVF(12%,8yrs) = $2,000*(1+.12)8 = $2,000*2.476 = $4,952
4) If in the above problem the interest is Simple Interest then Future Value wil be as follows :-
annual Interest = $2,000*12% = $240
Total Interest for 8 years = $240*8 = $1,920
Total Future Value after 8 years = $2,000+$1,920 = $3,920