Question

Seth borrows X from Tina and agrees to pay it back over 20 years using the sinking fund method. At the end of each year, Seth will deposit 400 into the sinking fund, as well as pay Tina the interest on the loan. If Tina charges Seth an annual effective interest rate of 6% and the sinking fund gains an annual effective interest rate of 3%, then what is the outstanding balance immediately after the 12th payment is made?

Answer 1

Answer:

The outstanding balance immediately after 12 years is $5,071.34.

Explanation:

Amount available in sinking fund account at the end of 12 years is given by:

( S ) = D*( (1+r)12 - 1 )/r

Where :

D = annual deposit at the end of every year = $ 400

r = interest earned on the depost = 3%

then:

S = 400 * ( ( (1+3%)12 - 1 ) / 3%)

   = $ 5,676.81

it is also mentioned that the sinking fund amount balance at the end of 20 years should be equal to repay the principal amount borrowed

so, sinking Fund at the end of 20 years would be :

T = D * ( (1+r)20 - 1 ) / r

   = 400 * ( ( (1+3%)20 - 1 ) / 3%)

  = $ 10,748.15

So, Seth has borrowed $ 10,748.15 from Tina which has to be paid at the end of 20 years.

At the end of 12 years his sinking fund balance would be equal to $ 5,676.81

As, he keeps paying interest regualarly every year at the end of 12 years the outstanding balance would be

= (Total amount borrowed) - (Sinking Fund at the end of 12 years)

= $ 10,748.15 - $ 5,676.81

= $ 5,071.34

Therefore, The outstanding balance immediately after 12 years is $5,071.34.