2 Assume that you need $1,000 four years from today (Janu ary 1) . Your bank com

Question

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

Answer 1.

Payment after 4 years = $1,000
Annual Interest Rate = 8%

Payment after 1 year * (1 + Interest Rate)^3 = Payment after 4 years
Payment after 1 year * 1.08^3 = $1,000
Payment after 1 year = $793.83

Answer 2.

Annual Payment * FVIFA(8%, 4) = $1,000
Annual Payment * (1.08^4 - 1) / 0.08 = $1,000
Annual Payment * 4.506112 = $1,000
Annual Payment = $221.92

Answer 3.

Option 2:

$750 after 1 year

Future Value = $750 * 1.08^3
Future Value = $944.78

So, you should select Option 1 of $221.92 every year and we will not have required payment after 4 years if we choose Option 2.

Answer 4.

Let interest rate required to earn be i%

Payment after 1 year * (1 + i)^3 = Payment after 4 years
$750 * (1+i)^3 = $1,000
(1+i)^3 = 1.3333
1+i = 1.1006
i = 0.1006 or 10.06%

So, you should earn an interest rate of 10.06%

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