Ch 13

Question 1

Compounding Exercise 1:

If I invest $60,000 at 6.5% interest, how much will be available when I retire in 12 years? Do the keystrokes.

Don’t forget to clear your registers first.

Answer 1

f CLEAR FIN

12 n

6.5 i

60000 CHS PV

FV

127,745.77

Question 2

If I put $1,000 in the bank every year for 5 years, at 3.5% interest - how much will I have? Please follow along and input these keystrokes into your own calculator.

Answer 2

First clear the financial registers - f CLEAR FIN.

[g] [BEG]

5 n

3.5 i

1000 CHS PMT

FV

Answer 5,550.15

Question 3

Compounding Exercise 2:

You invest $3,500 per year into a fund that pays 4.25% interest. What will it accumulate to in 8 years?

Answer 3

f CLEAR FIN.

[g] [BEG]

8 n

4.25 i

3500 CHS PMT

FV

33,921.37

Question 4

How much do I have to put aside each year, at 7% interest, to accumulate $9,000 to replace a roof in 8 years?

Answer 4

f CLEAR FIN

[g] [BEG]

8 n

7 i

9000 CHS FV

PMT

819.82

Question 5

Our homeowner’s association will need $50,000 in 9 years replace the swimming pool. How much needs to be set aside in a reserve fund each year if we can invest it at 5.5%? Do the keystrokes, using the last problem as a model. Click to the next page to see the answer.

Note: As stated earlier, the table provided assumes an end of period payment not beginning of period payment. To get the correct answer, you must again use the [BEG] function.

Answer 5

f CLEAR FIN

[g] [BEG]

9 n

5.5 i

50000 CHS FV

PMT

4,210.40

Question 6

What’s the value today of the right to receive $5,000 in 5 years, discounted at 8%?

Answer 6

Present Value (PV). We already know the future value, time period, and interest rate. Let’s enter them first then press PV.

f CLEAR FIN

5 n

8 i

5000 CHS FV

PV

3,402.92

Question 7

You want to purchase a bond that matures at $50,000 in 15 years. If it is discounted at 4.65% interest, how much will you have to pay now?

Answer 7

f CLEAR FIN

15 n

4.65 i

50000 CHS FV

PV

25,286.08

Question 8

What is the present value today of an $88,000 mortgage with 8% annual interest-only payments for 14 years?

Answer 8

f CLEAR FIN

88000 ENTER

.08 X

7040 (this is the annual interest payment you will receive - it is entered into the PMT key)

14 n

8 i

7040 CHS PMT

88000 CHS FV

PV

88,000

Now let’s see what the value is if we use a 10% discount rate.

Simply enter 10 into the “i” key then press the PV key

the display will show 75,034.63 which is the present value of the cash flows at a 10% discount rate.

Question 9

How much should an investor pay for a promissory note which is fully amortized with equal annual payments of $12,500 for 10 years, discounted at 12%? With this structure, there would be no balance left at the end of 10 years so the future value (FV) would be zero.

Answer 9

f CLEAR FIN

10 n

12 i

12500 CHS PMT

PV

70,627.79

Question 10

If we have a mortgage in the amount of $123,000 with annual payments for 20 years, at 6% interest, how much are the annual payments?

Answer 10

f CLEAR FIN

20 n

6 i

123000 CHS PV

PMT

10,723.70

Question 11

Assume a $82,000 mortgage with monthly payments for 25 years, at 8.35% interest. First let’s calculate the monthly payments.

Answer 11

f CLEAR FIN

25 g n

8.35 g i

82000 CHS PV

PMT

652.02

Question 12

Assume a $118,500 mortgage, at 6.5% with a monthly payment of $883.50. For how many years was the original mortgage written?

Answer 12

f CLEAR FIN

6.5 g i

118500 CHS PV

883.50 PMT

n

240

The answer is 240 - but that is the number of months.
12 ÷
The answer is 20 years.

Question 13

Assume a 27-year mortgage with a monthly payment of $1,255.74 and a 9.2% interest rate. What was original amount of the mortgage?

Answer 13

f CLEAR FIN

27 g n

9. 2 g i
10. 74 CHS PMT

PV

150,000

Question 14

We have a $212,750 mortgage, for 30 years and the monthly payment is $1,487.58. What is the interest rate?

Answer 14

f CLEAR FIN

30 g n

212750 CHS PV

1487.58 PMT

i

0.63

So, the answer is .63. But wait a minute – that is only the interest per month! We have to multiply by 12 to get the annual interest rate.
12 x

7.50

The real answer is that the interest rate is 7.5% per year.

Question 15

You can afford payments of $750 a month and you have a $25,000 down payment. The bank will give a mortgage for 30 years, at 6.8% with monthly payments. How expensive a house can you buy?

Answer 15

f CLEAR FIN

30 g n

6.8 g i

750 CHS PMT

PV

115,043.88

25000 +

140,043.88

With your $750, you would qualify for a mortgage of just over $115,000. Add in your down payment of $25,000 and you should be able to swing a house up to about $140,000.

Question 16

You have a mortgage of $112,500 with a 25-year term and a 7.2% annual interest rate, with monthly payments. However, there will be a balloon payment due at the end of year 5. How much will that be (the amount of the remaining balance of the loan at that point)?

Answer 16

First, we work through the sequence to find the PMT.

f CLEAR FIN

25 g n

7.2 g i

112500 CHS PV

PMT

809.54

Then we leave all the information in the rest of the registers but change the entry in the n register to 5 years and ask for the future value after 5 years.

5 g n

FV

102,818.06

Therefore, the remaining balance at the end of 5 years of the 25-year scheduled payout, to be paid off as a lump sum balloon payment, would be $102,818.06.