1. (a) If you deposit $17,500 in the bank today, what is its future value at the end of twelve years if it is invested in an account paying 4.80% interest (annual compounding, or APR)? (b) What is the present value of $17,500 to be received in twelve years if the appropriate interest rate is 4.80% APR? 2. We sometimes need to find how long it will take a sum of money (or anything else) to grow to some specified amount. Note that you should enter PV as a negative and FV as a positive. (a) For example, if a company's sales are growing at a rate of 4.80% per year, approximately how long will it take sales to triple? Show your answer to 2 decimals (x.xx years). If you are not sure how to work this, go back to this week's practice problems. Do not approximate using the "rule of "72". If you are in doubt here, go back to the practice problems where double/tripling is discussed. (b) If you want an investment to double in twelve years, what interest rate must it earn? Show your answer to 2 decimals (x.xx%). Visualization for problem 3 Investing on a regular basis for 30 years In retirement, withdrawing funds for 25 yrs you 3. (a) You are saving for retirement, and you can afford to save $14,400 every year, starting one year from today. If you invest for 30 years at an annual interest rate of 5.25% per year, how much will have saved for your retirement? Hint, this is the FV of an annuity. You may want to solve parts (c) and (e), then come back and solve (b) and (d), which are annuities due. (b) How much would you have in your retirement account if you began these same 30 annual payments immediately? Hint: This is now the FV of an annuity due.

1. (a) If you deposit $17,500 in the bank today, what is its future value at the end of twelve years if it is invested in an account paying 4.80% interest (annual compounding, or APR)? (b) What is the present value of $17,500 to be received in twelve years if the appropriate interest rate is 4.80% APR? 2. We sometimes need to find how long it will take a sum of money (or anything else) to grow to schme specified amount. Note that you should enter PV as a negative and FV as a positive. (a) For example, if a company's sales are growing at a rate of 4.80% per year, approximately how long will it take sales to triple? Show your answer to 2 decimals ( x-xx years). If you are not sure how to work this, go back to this week's practice problems. Do not approximate using the "rule of "72": If you are in doubt here, go back to the practice problems where dotrblemipling is diseussed (b) If you want an investment to double in twelve years, what interest mte must it earn? Show your answer to 2 decimals (x.xx%). Visualisarion for pnoblem 3 Investing on a regular basis for 30 years in retirement, withdrawing funds for 25yts 3. (a) You are saving for retirement, and you can afford to save $14,400 every year, starting one year from today, If you invest for 30 years at an annual interest rate of 5.25% per year, how much will yor and (e), then come back and solve (b) and (d), which are anmuities due. (b) How much would you have in your retirement account if you began these same 30 annual payments immediately? Hint. This is now the FV of an annuity due