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

(I) $ 1,490.30

(II) $ 1,558.68

(III) $ 1,490.30

(IV) $ 1,369.84

Step-by-step explanation:

(I) French system:

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV 10,000

time 10

rate 0.08

`10000 / (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 / ((1+r)^(time) -1)/(rate) = C\\`

FV 10,000

time 10

rate 0.06

`10000 / ((1+0.06)^(10) -1)/(0.06) = C\\`

C $ 758.680

Total: $1,558.68

`FV / ((1+r)^(time) -1)/(rate) = C\\`

FV 10,000

time 10

rate 0.08

`10000 / ((1+0.08)^(10) -1)/(0.08) = C\\`

C $ 690.295

Total $ 1,490.30

`FV / ((1+r)^(time) -1)/(rate) = C\\`

FV 10,000

time 10

rate 0.12

`10000 / ((1+0.12)^(10) -1)/(0.12) = C\\`

C $ 569.842

Total $1,369.84