Question

You open an investment account with $6,000 and must invest an additional $6,000 at the end of the year and every year there after for 35 years. At the end of the 36th year you want to withdraw from the account (you do not make an additional payment in the 36th year).

How much money has accrued if the interest rate paid is 5% per year?

Answer 1

Given about an investment,

Open balance = $6000

additional annuity payment of $6000 at the end of year for 35 years.

Interest rate r = 5%

So, this can be considered as an single annuity where 1st payment starts today of PMT = $6000 for next t = 36 years at the beginning of the period.

So, Value of this annuity at year 36 can be calculated using FV formula of annuity due.

FV = PMT*(1+r)*((1+r)^t - 1)/r = 6000*1.05*(1.05^36 - 1)/0.05

=> Future value at year 36 is $603768.83

So, amount accrued at the end of 36 years is $603769