I am so stuck on these questions on interest been working them for 2 days now, please help!?

Question

1. You have set up an ordinary annuity that will pay you $650.00 a month for the next 25 years. You will earn interest at a rate of 5.5% compounded monthly. What amount did you invest to accomplish this goal?

2. If an annuity was set up for semi-annual payments at the end of each period in the amt of $1350, what would be the value of this annuity after 15 1/2 yrs with interest compounded semiannually at a rate of 4%?

3. A company requires the amount of $850,000 in twenty(20) years to retire a bond issue. Assume they earn 5% interest compounded quarterly. What amount would they have to pay quarterly to be able to retire this debt in 20 years?

Answer 1

1. In this question, you are looking for the present value of the money you invested.

Present Value = ?
Future Value = 0
Payments = 650.00
Interest = 5.5%
Compounding Periods = monthly = 12
Payment Periods = monthly = 12
Number of Payments = 12 x 25 = 300

The formula is:

PV = PMT( [1 - (1+i)^-n] / i )

So plugging our information into the formula we have:

PV = 650( [ 1 - (1 + (0.055/12)^-300 ] / (0.055/12) )
PV = 650( [ 1 - (1.004583333)^-300 ] / 0.004583333 )
PV = 650(0.746365 / 0.004583333)
PV = 105 848.11

Therefore, you invested $105 848.11

2. This time, you are looking for the future value of the money.

Present Value = 0
Future Value = ?
Payments = 1350
Interest = 4%
Compounding Periods = semi-annually = 2
Payment Periods = semi-annually = 2
Number of Payments = 2 x 15.5 = 31

The formula in this case is:

FV = PMT( [(1+i)^n - 1] / i )

So plugging in our values we get:

FV = 1350( [(1+(0.04/2))^31 - 1] / (0.04/2) )
FV = 1350( [(1+(0.02))^31 - 1] / (0.02) )
FV = 1350( [(1+(0.02))^31 - 1] / (0.02) )
FV = 1350( 0.847588816 / (0.02) )
FV = 57 212. 25

Therefore, after 15.5 years of 1350 semi annually, you would have accumulated $57,212.25

3. Now you are looking for the value of the payments.

Present Value = 850 000
Future Value = 0
Payments = ?
Interest = 5%
Compounding Periods = quarterly = 4
Payment Periods = quarterly = 4
Number of Payments = 20 x 4 = 80

We have to rearrange the formula for the present value.

PV = PMT( [1 - (1+i)^-n] / i )
PMT = PV / ( [1 - (1+i)^-n] / i )

Then, subbing in the values we get:

PMT = 850000 / ( [1 - (1+(0.05/4))^-80] / (0.05/4) )
PMT = 850000 / ( [1 - (1+(0.0125))^-80] / (0.0125) )
PMT = 850000 / ( [0.629833213] / (0.0125) )
PMT = 850000 / 50.38665706
PMT = 16869.55

Therefore, they would have to make payments of $16 869.55 in order to retire the debt in 20 years.

Answer 2

Remember a few things. You take your amount of money and divide the principal by the number of payments dependent on how its compounded. Also, you multiply the exponent by the number that you divided your principal by. For example, a principal of $4,000 compounded quarterly at 5% would look like this: 4000/4 x 1.005(to the power of 4). That's how its done. Good luck.

Answer 3

I'd advise splitting up your homework questions into 3 separate questions.
Answering 3 questions for only 2 points with a potential of 10 is not a motivator as answers the questions separetly. 6 points for answering 3 questions, with a max potential of 30 points.

Answer 4

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Answer 5

Compare rates free

Answer 6

This is a combination math Finance Question, If you have access the excel or lotus 123, try using the formula's for present or future value, and Please get some finance training be4 trying this on your own.

Answer 7

Just download an amortization calculator.