Question

For tax reasons, your client wishes to purchase an annuity that pays $60,000 each year for 11 years, with the first payment in one year. At an interest rate of 12% and focusing on time value of money without consideration of any fees, how much would the client need to invest now?
Equivalent problem structure (in neutral time-value-of-money terms): What is the present value of an annuity that pays $60,000 each year for 11 years, assuming a discount rate of 12% and the first payment occurs one year from now? Equivalent problem structure (as a borrower): How much could you borrow today in exchange for paying back $60,000 each year for 11 years, assuming an interest rate of 12% and the first payment occurs one year from now?

Answer 1

Answer:

$356,261.95

Explanation:

Interest rate per annum = 12%

No of years = 11

No of corresponding per annum = 1

Interest rate per period = 12% (12%/1)

No of period = 11

Payment per period = $60,000

1.12^11

Investment today = P * [1 - (1/(1+r)^n)]/r

Investment today = 60,000 * {1 - (1/(1+0.12)^11)] / 12%

Investment today = 60,000 * {1 - (1/3.47855) / 0.12

Investment today = 60,000 * {1 - 0.2874761) / 0.12

Investment today = 60,000 * 0.7125239/0.12

Investment today = 60,000 * 5.937699167

Investment today = 356261.95002

Investment today = $356,261.95