Computing present values of single amounts and annuities compute the present value for each of the following amounts. round answers to the nearest dollar.

a. $120,000 received 10 years hence if the annual interest rate is: answer 1). 10% compounded annually. answer 2). 10% compounded semiannually.

b. $2,000 received at the end of each year for the next eight years discounted at 8% compounded annually.

c. $800 received at the end of each six months for the next 15 years if the interest rate is 10% per year compounded semiannually.

a. 1)$46,265 ; 2) $45,227

b. $11,493

c. $12,298

Explanation:

Please find the below for explanations and calculations:

The formula to calculate present value of single amount is: PV = FV/ (1+i)^n where PV is present value, FV is future vale, i is applied discount rate, n is number of discounting period;

The formula to calculate present value of annuity is: PV = (C/i) / [ 1 - (1+i)^(-n)] where PV is present value, i is applied discount rate, n is number of discounting period, C is the amount receipt at each time in the annuity.

a. 1) 120,000 / 1.1^10 = $46,265

   2) 120,000 / (1+10%/2)^(10x2) = 120/1.05^20 = $45,227

b. (2,000/8%) x [ 1 - (1+8%)^(-8) ] = $11,493

c. [800 / (10% /2)] x [ 1- (1+(10%/2))^-30 ] = $12,298  

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