Please show all work or inputs, and carry all dollar amount out to the nearest p

Question

Please show all work or inputs, and carry all dollar amount out to the nearest penny, and all interest rates out to the nearest 1/100th of a percent.

1. If you save $150 per month for the next ten years, $225 per month for the following 10 ten years, and $350 per month for the following ten years, how much will you have 30 years from now assuming that the account earns 8%. Assume beginning of month payments.

2. If an insurance company offers you annuity payments of $40,000 per year for the first 10 years of retirement and $50,000 per year for the next 10 years, what would you be willing to pay for this annuity if you have a required rate of return of 7.6%? Assume beginning of year payments.

3. You just bought a car and borrowed $22,000 from the bank to help with the purchase. Your monthly payments will be $415 for five years. What is the annual rate of interest you are paying on this loan and what will be the remaining principal immediately after the first payment is made?

4. You have decided to start saving for your daughter’s wedding, which you estimate will cost about $20,000. You will start making $300 monthly payments exactly one month from today into an account earning a 4% annual rate of return. How long (to the nearest month) will it take you to have the money for the wedding?

5. Explain why the future value of an annuity due is greater than the future value of an ordinary annuity (all else being equal), and why the present value of an annuity due is always higher than the present value of an ordinary annuity (again, all else being equal).

Explanation / Answer

1) AS THE PAYMENTS WILL BE MADE AT THE BEGINNING OFTHE MONTH

ASSUMED THAT THE INTEREST RATE IS PER ANNUM

INTEREST=8%/12=.0067,N=10*12=120

=150[(1+.0067)120-1)/0.008](1+.0067)=150*183.58*1.0067=$27722

SIMILARLY SAVING 225 PER MONTH=225*183.58*1.0067=$41582

350 PER MONTH=350*183.58*1.0067=$64684

TOTAL=$133988

4)FUTURE VALUE OF ANNUITY DUE IS GREATER THAN ANNUITY ORDINARY BECAUSE THE PAYMENT STARTS IN THE FORMER CASE IMMEDIATLY/BEGINNING AND IN CASE OF LATER AFTER THE SCHEDULED PERIOD THAT IS AT END.

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