Answer to Question #193956 in Financial Math for King

Question

Sinking fund schedule

A ₱50,000 debt is to be repaid at the end of one year. The debtor establishes a sinking fund that earns 8% interest compounded quarterly. Construct a sinking fund schedule

Answer 1

yearly effective rate(i)$=((1+\dfrac{r}{n})^n -1)\times 100$

r= periodic compounding rate

n= no. of periods or compounding frequency

yearly effective rate $(i)=((1+\dfrac{.08}{4})^4 -1)\times 100=8.243$ %

now we can calculate yearly payments as follows

$E(\dfrac{(1+i)^t – 1)}{i}) = FV$

Where

E=50000

i = yearly effective rate =8.243%

t= total period of fund=1 year

FV= Future Value of Fund

hence we have

$50000\times (\dfrac{(1.08243)^1 -1)}{0.08243}=FV$

solving this and we get 

FV=50000

now, the Sinking fund Schedule is as follows-

Yearly debt=50000

Interest at the end of year=8.234%

Future value of fund=50000