Consider the following two saving schemes.
I Option 1: On 31 December of year 0, a grandmother opens a bank account with 1,700$ for
her daughter. On 31 December of each year (excluding year 0), she pays ’interest’, that is,
she deposits an amount that corresponds to 2.5% of the account balance on that day into the
account. Further, in each year (excluding year 0), immediately after the ’interest payment’
on 31 December, she deposits an additional 130$ to the account. Let An denote the amount
of money in the account on 31 December of year n (after interest payment and deposit).
I Option 2: On 31 December of year 0, a grandmother opens a bank account with 1,700$
for her granddaughter. Starting in year 1, she deposits 125$ into this account on 1 January
of every year. On 31 December of each year (excluding year 0), she pays ’interest’, that is,
she deposits an amount that corresponds to 2.5% of the account balance on that day to the
account. Let Bn denote the amount of money in the account on 31 December of year n (at
close of business, that is, after the interest was paid).