1. Consider a 1-Year $10,000 CD
A. The future value of a $10,000 CD that has a maturity of 1 year at maturity with 10% interest is $11,000. Financial Calculator Inputs: $ -10,000=PV, 1=N, I=10, FV=? ($11,000) B. The future value of a 1-year, $10,000 CD after one year at an interest rate of 5.0% is $10,500. Financial Calculator Inputs: $-10,000=PV, 1=N, 5=I, FV=? ($10,500) The future value of a 1-year, $10,000 CD after one year at an interest rate of 15.0% is $11,500. Financial Calculator Inputs: $-10,000=PV, 1-N, 15=I, FV=? ($11,500) C. The effective annual rate of First National Bank’s CD offering a 10% nominal interest rate compounded semiannually is 10.25%.
Calculations: (1+.10/2)^2 -1
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(14.3547)
4. Now considering a second alternative with 5 annual payments of $2,000 each. The payments are assumed made at the end of each year.
A. The type of annuity in which payments are made at the end of each year is referred to as an Ordinary Annuity (Annuity in Arrears) B. The future value of the annuity with payments of $2,000 each year at the end of 5 years is $12,210.20 with an interest rate of 10% compounded annually. Financial Calculator Inputs: $ -2,000=PMT, 5=N, 10=I, FV=? ($12,210.20) C. The future value of an annuity with yearly payments of $2,000 for five years deposited at the First National Bank which offers semiannual compounding of a nominal 10% interest rate is $12,271.11.
Calculations: EAR= (1=.10/2)^2 -1 =10.25%
Financial Calculator Inputs: 10.25=I, $2,000=PMT, 5=N, $0=PV, FV=? ($12,271.1147) D. Under 10% annual compounding of interest for 5 years, an annuity would require five equal payments of $3,275.95 in order to accumulate $20,000 after 5 years.
Financial Calculator Inputs: $20,000=FV, 10=I, 5=N, $0=PV, PMT=? ($-3,275.95)
E. A lump sum of $7,581.57 would be required if deposited today to compound to the equivalent of $12,210.20 in five years assuming an annual interest rate of 10% Financial Calculator Inputs: $12,210.20 (from part B)=FV, 10=I, 5=N, PV=? ($-7,581.57) F. Assuming
academic year interest rate of 3.76 percent would pay a 5,032 dollars interest over 10 years,
a) Assuming the opportunity interest rate is 6%, what is the present value of the second alternative?
B. The present value of an annuity is unaffected by the number of the annuity payments.
14. How close does the terminal value in part 2 get to the present value using the growing annuity formula in part 3?
a. Starting with $20,000, how much will you have in 20 years if you can earn 5% on your money?
a. What is the CD’s value at maturity (future value) if it pays 10 percent annual interest?
8. What is the net present value of the following cash flows discounted at 12%?
It is much easier to calculate the FV of annuity when the payments are made at semiannual compounding, the periodic rate is simply the nominal rate divided by two (number of compounding periods per year). Thus, the result should be:
10. An investment of $1,000 today will grow to $1,100 in one year. What is the continuously compounded rate of return?
2. If you had a payment that was due you in 5 years for $50,000 and you could earn a 5% rate of return, how much
A person deposited $500 in a savings account that pays 5% annual interest that is compounded yearly. At the end of 10 years, how much money will be in the savings account? (Bluman, A. G. 2005, page 230).
In this case, to get the present value (PV), we can use the formula of growing annuity.
1. Assume that at retirement you have accumulated $825,000 in a variable annuity contract. The assumed investment return is 5.5% and your life expectancy is 18 years. What is the hypothetical constant benefit payment?
First we need to get the present value of the annuity for the 1,500 semiannual PMTs at year 14
Most People have money in a savings account and wonder how to figure out the actual interest rates or the APR (annual percentage yield). To find the amount of interest you would use this formula: P (principle) x R (rate) x T (time) = I (interest)