Question

Show your work.  Suppose that John takes a loan of 7000 today and pay 1000 in 3 years and he takes another loan of 2000 in 4 years. He plans to pay everything in 5 years. If the interest rate is 12 compounded monthly, what is his payment in 5 years?

Answer 1

Formula for compound interest is:

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

A = Final amount

P = Principal amount = $ 7,000

r = Rate of interest = 0.12

n = Number of compounding in a year = 12

t = Number of years amount invested = 3

Loan amount in year 3,

A = $ 7,000 x (1+0.12/12)12x3

     = $ 7,000 x (1+0.01)36

   = $ 7,000 x (1.01)36

      = $ 7,000 x 1.43076878359158

   = $ 10,015.3814851411 or $ 10,015.38

Final amount in year 3 = $ 10,015.38 - $ 1,000 = $ 9,015.38

Final amount in year 4 = $ 9,015.38 x (1.01)12 + $ 2,000

                                        = $ 9,015.38 x 1.12682503013197 + $ 2,000

                                        = $ 10,158.7558401512 + $ 2,000 = $ 12,158.7558401512

Final amount in year 5 = $ 12,158.7558401512 x 1.12682503013197

                                         = $ 13,700.7904159456 or $ 13,700.79

Final payment of John in year 5 is $ 13,700.79