Question

Company Y wants to deposit money in a bank account in order to be able to withdraw €50,000 after the first three years, and €60,000 after additional two years. The bank offers 6% annual interest rate for the first three years and 8% interest for the following years. What amount should Y deposit now?

Answer 1

Money needs to be withdraw after 3 years 50,000

Money needs to be withdraw after 2 additional years 60,000

Annual interest rate for initial 3 years 6%

Annual interest rate for After 3 years 8%

Assume the interest is compounded

Compound Interest formula we will use here.

Amount = Principal (1+ r/100)n

We will do back ward calculation over here. so, Amount needed after additional 2 years 60,000

Amount= 60,000

Principal= ?

Rate= 8%

n(time)= 2years

60,000=Principal ( 1+ .08/100) 2

60,000= Principal [(108/100) x (108/100)]

Principal= 60,000/1.1664

Principal = 51441 (Rounded off)

Thus amount at the end of 3rd year should be 51,441 after withdrawing 50,000

which means at the end of 3rd year amount should be = 50,000+51,441 = 101,441

Amount Required at the end of third year is 101,441

Amount= 101,441

Principal= ?

Rate= 6%

n(time)= 3 years

101,441=Principal ( 1+ .06/100) 3

101,441= Principal [(106/100) x (106/100) x (106/100)]

Principal= 101,441/1.191016

Principal = 85,172 (Rounded off)

Thus Amount should Y deposit now = 85,172

I have prepared one table flow to understand the workings well, please check the table below for better understanding.

Years	Flow	Interest Rate	Amount
0	Invest		85172
1	Interest	6%	90282
2	Interest	6%	95699
3	Interest	6%	101441
3	Withdraw		-50000
3	Interest	6%	51441
4	Interest	8%	55557
5	Withdraw	8%	60001