Question

You are an insurance company and have sold an annuity to a customer.
The annuity pays 360 monthly payments (the same each month) starting 12 months from today.
The monthly payments are $500 per month.
If your firm earns 5.00% APR (compounded monthly), on its investments,
how much does it have to invest today to just cover the cost of the annuity?

Answer 1

Annuity payment will start after 12 months,

Monthly Payment = $500

Interest Rate = 5% compounded monthly

Number of payments = 360

Value of annuity 12 months from today,

Using TVM calculation,

PV = [FV = 0, T = 360, PMT = 500, R = 5]

PV = $93,140.81

Annual Interest Rate = (1 + 0.05/12)¹² - 1

Annual Interest Rate = 5.116%

Value of Annuity today = 93140.81/(1 + 0.05116)

Value of Annuity today = $88,607.64

So, $88,607.64 must be invested today to cover the cost of annuity.

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