Question

How much should I invest today in a bank account that offers an annual interest rate of a 12% compounded monthly, in order to be able to afford infinite monthly payments, the first one of them to be of 200 €, and the amount of the further payments increasing in a 0.2% month after month?

Answer 1

Hi

This is an example of perpetuity payment

where first payment C= Euro 200

growth rate g= 0.2%

rate r = 12%/12 = 1% monthly

Current invest amount = present value =?

Present value of growing perpetuity = C/(r-g)

=200/(1%-0.2%)

= 200/0.8%

= Euro 25,000

Hence you should invest euro 25,000 today.

Thanks