Question

A personal account earmarked as a retirement supplement contains $242,300. Suppose $200,000 is used to establish an annuity that earns 6%, compounded quarterly, and pays $4500 at the end of each quarter. How long will it be until the account balance is $0? (Round your answer UP to the nearest quarter.)

Answer 1

The retirement supplement of a personal account contains

$242,300 and the annuity is $200,000 that earns 6% compounded

quarterly and pays $4500 at the end of each quarter.

The present value for a payment of $A that is to be made at the end

of each period for n years with k periods (k=4 since quarterly) from an account that earns interest at the rate of i per period is,

An = R *((1-(1+i)^n*k)/i)

The future value of an annuity is given as, An = 200, 000

The payment of $4500 pays at the end of each quarter.

R = 4500

The interest that earns at a rate of 6% compounded quarterly is,

i=6/100*1/4 = 0.015

Use the formula for present value of payment,

An = R *((1-(1+i)^n*k)/i)

Substitute 4500 for R, 0.015 for i and 200, 000 for An in the above

formula.

200, 000 = 4500 *(1-(1+0.015)^-n*4)/0.015)

                N=18.46