At the end of the first 10 years, the amount in the account is
$2000*[1+1.08+1.08^2+1.08^3+ ... + 1.08^9]
= $2000 [ (1.08^10 - 1) / (1.08 - 1) ]
= $2000 (1.1589/0.08) = $28973.12
Interest then accrues for the next 5 years, bringing the total to
$28973.12 * [ (1.08)^5 ] = $42571.03
The "cents" in this calculation are unreliable, since the bank may round off to the nearest cent at the end of each compounding period.
