Wages earners have as a result of the Covid-19 pandemic been given the option to utilize otherwise frozen savings accounts. This is to stimulate the German economy.

Every wage earner has had their accounts unfrozen with the new system in 2020. The accounts will with and from the year 2021 earn interest and the accumulated worth of the account will only be paid out on the on the day that the account owner earns the right to a people's pension. Income taxes only apply to the account during a payout.

You are tasked with advising three different wage earners, they all have savings accounts which have been unfrozen. The overall dilemma for these tree wage earners is weather they should take out their savings accounts now or wait until they gain the right to a peoples pension.

In the answers you give, the following assumptions should be made.

Today is the 31. Of December 2020

There complete security meaning no risk in the market.

Selected effective annual market interest rates:

Rent from bank accounts is 0,00% until ultimo year 2026. After 2026 the rent is at 2,00%.

Overdraft is at 8,00%

Income from interest is taxed at 36%

Rent expense is taxed at 30%

Yearly tax-exempt interest on the frozen accounts (accounts that have not been paid out) is at 1,50%

Income taxes and consumption expenditures are calculated ultimo every year.

Yearly inflation is at 1,00% until the end of year 2026. After the year 2026 the inflation rate is at 2,00%

People born between the year 1963 and 1966 will gain the right to a peoples pension at the age of 68, (they become pensioners at the age of 68, unless stated otherwise)

Lars Rytter turns 55 today the 31. of December 2020. His savings account will payout 40.000 Euro(before taxes) if he decides to empty his account before he becomes a pensioner.

Lars Rytter finances himself using bank credit(overdraft) until the year 2034. The dept owed is currently 100.000 Euro. And the dept will grow until his 68^th birthday.

The dept will grow with the yearly interest rate(after taxes). On the 68^th year the dept will be reduced by the payout from the savings account.

Lars Rytter must pay a 42% income tax whether he choses to take the payout from his account, today or when he becomes a pensioner on his 68^th birthday.

Q.1

Assume that Lars Rytter choses to wait with withdrawing money from his account until he becomes a pensioner on his 68^th birthday. Calculate the size of his dept by the year 2033/34, after his savings account is merged with the account containing dept