Question

A four-year annuity of eight $6,600 semiannual payments will begin nine years from now, with the first payment coming 9.5 years from now. (Do not round intermediate calculations. Round the final answers to 2 decimal places. Omit $ sign in your response.)

If the discount rate is 10 percent compounded monthly, what is the value of this annuity five years from now?

Value of the annuity           $

If the discount rate is 10 percent compounded monthly, what is the value three years from now?

Value of the annuity           $

If the discount rate is 10 percent compounded monthly, what is the current value of the annuity?

Value of the annuity           $

Answer 1

Annual Interest Rate = 10.00% compounded monthly

Monthly Interest Rate = 10.00% / 12
Monthly Interest Rate = 0.83333%

Effective Annual Rate = (1 + Monthly Interest Rate)^12 - 1
Effective Annual Rate = (1 + 0.0083333)^12 - 1
Effective Annual Rate = 1.104713 - 1
Effective Annual Rate = 0.104713 or 10.4713%

Semiannual Interest Rate = (1 + Effective Annual Rate)^(1/2) - 1
Semiannual Interest Rate = (1 + 0.104713)^(1/2) - 1
Semiannual Interest Rate = 1.051053 - 1
Semiannual Interest Rate = 0.051053 or 5.1053%

Semiannual Payment = $6,600
Number of Payments = 8

Value of Annuity 5 Years from now = $6,600/1.051053^9 + $6,600/1.051053^10 + … + $6,600/1.051053^15 + $6,600/1.051053^16
Value of Annuity 5 Years from now = $6,600 * (1/1.051053)^8 * (1 - (1/1.051053)^8) / 0.051053
Value of Annuity 5 Years from now = $6,600 * 4.321206
Value of Annuity 5 Years from now = $28,519.96

Value of Annuity 3 Years from now = $28,519.96/1.051053^4
Value of Annuity 3 Years from now = $28,519.96 * 0.819411
Value of Annuity 3 Years from now = $23,369.57

Value of Annuity today = $23,369.57/1.051053^6
Value of Annuity today = $23,369.57 * 0.741741
Value of Annuity today = $17,334.17