Question

aquatech borrowed 430000 for an ew project at 16% apr compounded quarterly over 5 years wit payments 30000 made at the end of each quarter. how much will still be owing after 1 year?

Answer 1

Here the equation for compound interest is:

A = P (1 + r/n)^nt

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount =430000

r = Annual Nominal Interest Rate as a decimal = 0.16

t = Time Involved in years =5

n = number of compounding periods per unit t =4

Here the question is to find the debt after one year (or at the end of year 1)

Also, it is said that after each quarter 30000 is payed back, which means 30000 is excluded from the next compounding.

After first quarter:

A = 430000(1 + 0.16/4)^4*0.25

A= $ 447,200

After excluding $30000

A=$417200

After second quarter:

A = 417200 (1 + 0.16/4)^4*0.25

A = $ 433,888

After excluding $30000

A = $ 403,888

After third quarter:

A = 403,888 (1 + 0.16/4)^4*0.25

A = $ 420,043.52

After excluding $30000

A = $390043.52

After fourth quarter:- first year

A = 390043.52 (1 + 0.16/4)^4*0.25

A = $ 405,645.26

After excluding $30000

A=$375645.26

Therefore, $375645.26 will still be owing after first year.