A $1 payment is to be made each year for 22 years. The effective annual rate...

A $1 payment is to be made each year for 22 years. The effective annual rate of interest is 8.25%. If the first payment is one year from now, the present value of these payments is $10.

In which one of the following ranges is the present value of these payments if the first payment is 22 years from now?

A. <$1.80

B. >=$1.80 and <$1.86

C. >=$1.86 and <$1.92

D. >=$1.92 and <$1.98

E. >=$1.98

Expert Solution

If 1st payment is made 1 year from now, value of these payments is $10

If 1st payment is made 22 years from now instead of 1 year from now, then present value would be discounted for 21 years more.

Therefore present value if 1st payment is made 22 years from now = $10 / (1+8.25%)²¹

Therefore present value if 1st payment is made 22 years from now = $10 / 1.0825²¹

Therefore present value if 1st payment is made 22 years from now = $10 / 5.2843

Therefore present value if 1st payment is made 22 years from now = $1.892

Therefore, Option C is correct.

jeff jeffy answered 2 years ago

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