Question

I need help with question 1.3 on a constant growing annuity?

Problem 1.2 (6%) In the table below, information about the market index, asset A and the risk-free asset on a given normal market are stated. The risk-free rate next year is 0.6%. DKK Asset Cash flow year 1 Recession Boom Market price (DKK) today (t=0) 1,500 Market index Asset A Risk-free asset 2 1,200 225 975 2,100 1,125 975 Calculate the price of asset A. Hint: First determine the price of the risk-free asset. Problem 1.3 (13.5%) Ellen has just turned 27 and got her first job. She has therefore decided to start a pension plan. Ellen has also decided that she will retire when she turns 62, i.e. the maturity of the pension plan is exactly 35 years. The pension plan will have monthly payments. Ellen expects her salary to rise all the years until retirement. Ellen will therefore increase her monthly payments with a constant growth rate of 0.2% per month. Ellen will pay the first amount of DKK 5,100 in exactly one month. The dis- count rate related to the pension plan is 0.08% per month. Calculate the balance (in DKK million) of the savings, when Ellen turns 62. Hint: Start calculating the PV of the savings and then compound. Page 7 of

Answer 1

PVOrdinary Annuity = (C/((r-g)/(f*100))*(1-((1+g/(f*100))/(1+r/(f*100)))^(n*f)))*(1+r/(f*100))^(n*f)

C = First cash flow

i = interest rate g = growth rate

n = number of payments I f = frequency of payment

FV = (5100/((0.96-2.4)/(12*100))*(1-((1+2.4/(12*100))/(1+0.96/(12*100)))^(12*35)))*(1+0.96/(12*100))^(12*35)

FV = 3889912.66