Saving annuities

(FV, Ordinary Annuity, annual) Give an annual opportunity cost of 10%, what is the future value of a $1,000 ordinary annuity for 10 years?

 $FV_{OA\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)$   $FV_{AD\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)\cdot\left(1+r\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)\cdot\left(1+r\right)$  

• $15,937

• $15,739

• $10,000

• $12,000

(FV, Ordinary Annuity, annual)What is the future value in 10 years of $1,500 payments received at the end of each year for the next 10 years? Assume an interest rate of 8%.

 $FV_{OA\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)$   $FV_{AD\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)\cdot\left(1+r\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)\cdot\left(1+r\right)$  

• $25,260

• $23,470

• $21,730

• $18,395

(PMT, Ordinary Annuity,annual)You open a savings account that pays 4.5% annually. How much must you deposit each year in order to have $50,000 five years from now?

Note: for PMT, shuffling is required.

 $FV_{OA\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)$   $FV_{AD\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)\cdot\left(1+r\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)\cdot\left(1+r\right)$  

• $8,321

• $9,629

• $8,636

• $9,140

(PMT, Ordinary Annuity, annual) How much must you deposit at the end of each year in an account that pays an annual interest rate of 20%, if at the end of 5 years, you want $10,000 in the account?

Note: for PMT, shuffling is required.

 $FV_{OA\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)$   $FV_{AD\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)\cdot\left(1+r\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)\cdot\left(1+r\right)$  

• $1,500

• $1,250.66

• $1,393.47

• $1,343.72

(Interest rate, Ordinary Annuity, annual) What annual interest rate would you need in order to have an ordinary annuity of $7,500 per year accumulate to $279,600 in 15 years?

Note: for interest rate, it is impossible to solve scientifically using calculus, the only way is to use try-and-error.

 $FV_{OA\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)$   $FV_{AD\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)\cdot\left(1+r\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)\cdot\left(1+r\right)$  

• 8.75%

• 10.2%

• 12.0%

• 14.0%

(FV, Ordinary Annuity,monthly)You are saving up for a down payment on a house. You will deposit $600 a month for the next 24 months in a money market fund. How much will you have for your down payment in 24 months if the fund earns 10% APR compounded monthly?

 $FV_{OA\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)$   $FV_{AD\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)\cdot\left(1+r\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)\cdot\left(1+r\right)$  

• $14,480

• $15,870

• $12,930

• $10,560

(PMT, Annuity Due, annual) The Wintergreens are planning ahead for their son’s education. He is eight now and will start college in 10 years. How much will they have to set aside each year starting right now to have $65,000 in 10 years if the annual interest rate is 7%?

Note: for PMT, shuffling is required.

 $FV_{OA\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)$   $FV_{AD\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)\cdot\left(1+r\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)\cdot\left(1+r\right)$  

• $4,704.55
  

• $4,396.76

• $3,975.89

• $4,624.55

(Interest rate, Annuity Due, annual) You are told that if you invest $11,100 per year for 19 years (all payments made at the beginning of each year), you will have accumulated $375,000 at the end of the period. What annual rate of return is the investment offering?

Note: pay attention to key words for annuity due - starting immediately, starting now, starting today, at the beginning of each.

Note: for interest rate, it is impossible to solve scientifically using calculus, the only way is to use try-and-error.

 $FV_{OA\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)$   $FV_{AD\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)\cdot\left(1+r\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)\cdot\left(1+r\right)$  

• 5.48%

• 4.58%

• 8.54%

• 4.85%

(FV, Ordinary Annuity, annual)If you require a 9% annual return on your investments, you would prefer $15,000 five years from today rather than an ordinary annuity of $1,000 per year for 15 years.

(Hint: comparing the two present values at time 0 or comparing the two future values at time 15 and try to maximize the return on investments).

 $FV_{OA\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)$   $FV_{AD\ }=\ PMT\cdot\left(\frac{\left(1+r\right)^{N\ }-\ 1}{r}\right)\cdot\left(1+r\right)=\frac{PMT}{r}\cdot\left(\left(1+r\right)^{N\ }-\ 1\right)\cdot\left(1+r\right)$  

• Prefer A - $15,000 five years from today
  

• Prefer B - $1,000 per year for 15 years