Question

A ten year loan of 10,000 at 8% annual effective can be repaid using any of the 4 following methods:

(I) Amortization method, with annual payments at the end of each year.
(II) Repay the principal at the end of ten years while paying the 8% annual effective interest on the loan at the end of each year. In addition, make equal annual deposits at the end of each year into a sinking fund earning 6% annual effective so that the sinking fund accumulates to 10,000 at the end of the 10th year.
(III) Same as (II), except the sinking fund earns 8% annual effective.
(IV) Same as (II), except the sinking fund earns 12% annual effective.
Rank the annual payment amounts of each method.

Answer 1

Answer:

(I)    $ 1,490.30

(II)  $ 1,558.68

(III) $  1,490.30

(IV) $ 1,369.84

Explanation:

(I) French system:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV 10,000

time 10

rate 0.08

$10000 \div \frac{1-(1+0.08)^{-10} }{0.08} = C$

C  $ 1,490.295

American system with payment of interest on the principal

and then, to a fund to generatethe principal at maturity

(II) 800 dollar of interest plus cuota to get 10,000 in the future

$FV \div \frac{(1+r)^{time} -1}{rate} = C$

FV 10,000

time 10

rate 0.06

$10000 \div \frac{(1+0.06)^{10} -1}{0.06} = C$

C  $ 758.680

Total: $1,558.68

$FV \div \frac{(1+r)^{time} -1}{rate} = C$

FV 10,000

time 10

rate 0.08

$10000 \div \frac{(1+0.08)^{10} -1}{0.08} = C$

C  $ 690.295

Total $ 1,490.30

$FV \div \frac{(1+r)^{time} -1}{rate} = C$

FV 10,000

time 10

rate 0.12

$10000 \div \frac{(1+0.12)^{10} -1}{0.12} = C$

C   $ 569.842

Total  $1,369.84