Question

Charlie Stone wants to retire in 30 years, and he wants to have an annuity of $1,000 a year for 20 years after retirement. Charlie wants to receive the first annuity payment at the end of the 31st year. Using an interest rate of 10%, how much must Charlie invest today in order to have his retirement annuity (round to the nearest $10)?

Answer 1

Answer:

Present value Due = $9,364.92

Explanation:

Given:

Number of payment (n) = 20

Periodic payment (PMT) = $1,000

Rate of interest (i) = 10% = 10/100 = 0.1

Present value of annuity = ?

Computation of Present value of annuity:

$Present Value = PMT [\frac{1-(1+i)^{-n}}{i}] (1+i)$

$Present Value = 1,000 [\frac{1-(1+0.1)^{-20}}{0.1}] (1+0.1)\\\\Present Value = 1,000 [\frac{1-(1.1)^{-20}}{0.1}] (1.1)\\\\Present Value = 1,000 [\frac{1-0.148643628}{0.1}] (1.1)\\\\Present Value = 1,000 [\frac{0.851356372}{0.1}] (1.1)\\\\Present Value = 1,000 [\frac{0.851356372}{0.1}] (1.1)\\\\Present Value = 9,364.92$

Present value Due = $9,364.92