Question

a) You invest $10,000. What annual return do you need to grow this investment to $20,000 over 19 years? Answer in percent, rounded to one decimal place. Don't include the % symbol in your answer.

b) You own a 28-year, 4.1% annual coupon bond with $1,000 face value. If the yield to maturity is 5%, how much is it worth? Round to the nearest cent.

c) If you take out an amortized loan of $27,000 with a 7 year term and 5.7% interest rate, what are the annual payments you need to make? Round to the nearest cent.

Answer 1

a.Information provided:

Future value= $20,000

Present value= $10,000

Time= 19 years

The question is calculated by computing the yield to maturity.

Enter the below in a financial calculator to compute the yield to maturity:

FV= 20,000

PV= -10,000

N= 19

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 3.72.

Therefore, the annual rate should be 3.72% for $10,000 to grow to 20,000.

b.Information provided:

Face value= future value= $1,000

Time= 28 years

Coupon rate= 4.1%

Coupon payment= 0.041*1,000= $41

Yield to maturity= 5%

The worth of the bond is calculated by computing the present value of the bond.

Enter the below in a financial calculator to compute the present value:

FV= 1,000

PMT= 41

N= 28

I/Y= 5

Press the CPT key and PV to compute the present value.

The value obtained is 865.92.

Therefore, the bond is worth $865.92.

c.Information provided:

Present value= $27,000

Time= 7 years

Yield to maturity= 5.7%

Enter the below in a financial calculator to calculate the annual payment:

PV= -27,000

I/Y= 5.7

N= 7

Press the CPT key and PMT to compute the annual payment.

The value obtained is 4,785.20.

Therefore, the annual payments I need to make is $4,785.20.