Question

a stock account $14.300. What is the APR on this loan? The EAR? 44. Annuity Values. You are planning your retirement in 10 years. You currently have $75,000 in a bond account and $300,000 in a stock acs You plan to add $6,000 per year at the end of each of the next 10 ve your bond account. The stock account will earn a return of 10.5 percent. the bond account will earn a return of 7 percent. When you retire, you play to withdraw an equal amount for each of the next 25 years at the end of ea year and have nothing left. Additionally, when you retire you will transfer your money to an account that earns 6.25 percent. How much can you withdraw each year?

Answer 1

Balance in Bond account = $75000

additional investment on bond account = $6000 at the end of each year for next 10 years.

Lets first calculate balance in bond account after 10 years

It is an ordinary annuity, so using formula of FV with interest rate = 7%

Fv = A*((1+r)^n - 1)/r

Final balance in bond account = 6000*((1.07^10) - 1)/0.07 + 75000*1.07^10 = 82898.69 + 147536.35 = $230435.04

Balance in stock account today = $300000

Interest earned on it is 10.5%

So, balance after 10 years = 300000*1.105^10 = $814224.25

total balance in the account at the time of retirement = 230435.04 + 814224.25 = $1044659.29

Now this money is shifted to an account that earn interest of 6.25%.

Let withdrawal amount at the end of each year for next 25 years be A, this is again an ordinary due annuity with

PV = $1044659.29, i = 6.25%, n = 25

So, using Formula A = (PV*r)/(1 - (1+r)^(-n))

So, A = 1044659.29*0.0625/(1 - 1.0625^(-25)) = $83671.59

So, a withdrawal of $83671.59 can be made at the end of each year for next 25 years.