7/25/2019 CH_BMW
1/2
a.
The balance of the loan is the present value of the future loan
payments. The
annual loan payments form an annuity of equal amount.
Present value of annuity of equal amount = Amount * {1 (1+r
!n
"#r
$oan amount = %&'''' ! %1)''' = %)'''
r = , = '.'
n = & years
-ence
%)''' = $oan payment * (1!1.'!'.' = $oan payment * .)
$oan payment = %)'''#.) = %1''/1./
b.
0eare2innin2 loanbalance 3nterest 4 , $oan payment
Principalpart
5n6in2 loanbalance
1 % )''' % ')' % 1''/1 % )1 % /'1
7 % /'1 % /)17 % 1''/1 % &)7' % /7
/ % /7 % 77) % 1''/1 % 81'& % 7)/7
% 7)/7 % 77) % 1''/1 % 88& % 18&&
) % 18&& % 1) % 1''/1 % / % 7'/
& % 7'/ % 7 % 1''/1 % 7'/ % '
59ercise
:uture value at the en6 of 6eposit perio6 = Amount 6eposite6 *
(1+rn
r = Perio6ical interest rate = 3nterest rate#;ompoun6in2 perio6s
per year = i#m
n = Total compoun6in2 perio6s =
