1 Suppose that today (January 1) you deposit ed $1,000 into a savings account th

Question

1 Suppose that today (January 1) you deposit ed $1,000 into a savings account that pays 8 percent.

1. If the bank compounds interest annually, how much will you have in your account three years from today ?

2. What would your balance be in three years if the bank used quarterly compound ing rather than annual compounding?

3. Suppose you deposited the $1,000 in four payments of $250 each on January 1 of the next four years, beginning one year from today . How much would you have in your account in four years when the last deposit is made as suming that interest is 8 percent compounded annually?

2 Assume that you need $1,000 four years from today (Janu ary 1) . Your bank compounds interest at an 8 percent annual rate .

1. If you wait one year (January 1 next year) to make a deposit, how much must the depo sit be for you to have a balance of $1,000 in your account four years from today ?

2. If you want to make four equal payments on each January how large must each of the four payments be to accumulate $1,000 if the first payment is made one year from today a nd the last payment is made four years from today ?

3. If your father were to offer either to make the payments you calculated in part b ($221.92) or to give you a lump sum of $750 on January 1 one year from today, which sh ould you choose?

4. If you deposit $750 in your account next January 1 , what interest rate, compounded annually, would you have to earn to have the nec essary $1,000 four years from today ?

5. Suppose you can deposit only $186.29 each of the next four years (beginning next January 1 ) , but yo u stil l need $1,000 when the last $186.29 deposit is made . At what interest rate, with annual compounding, must you invest to achieve your goal?

5. To help you reach your $1,000 goal, your father offe rs to give you $400 next January 1 . You will get a part - time job and make six additional payments of equal amounts each six months thereafter. If all of this money is deposited in a bank that pays 8 percent, compounded semiannually, how large must each of the six payments be?   

Explanation / Answer

Using the formula: FV = PV*((1+ periodic rate of interest)^number of periods), we will solve Q1:

1.1. FV = 1000*((1+0.08)^3) = 1259.71

1.2. FV = 1000*((1+(0.08/4))^(3*4)) = 1268.24

1.3.

Kindly ask the 2nd question seperately.

Year Amount FV @ 8%                   1         250.00 =250*((1+0.08)^3) = 314.93                   2         250.00 =250*((1+0.08)^2) = 291.6                   3         250.00 =250*((1+0.08)^1) = 270.00                   4         250.00 =250*((1+0.08)^0) = 250.00 Total                                              1,126.53

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