MATH SOLVE

3 months ago

Q:
# A fisherman borrowed 85,000 over 25 years at 13.5% p.a. interest compounded monthly. At the end of the seventh year, interest rate climbed to 15% p.a. compound and fisherman's repayments were increased to allow him to complete the repayments by the end of 25 years term.a. how much did the fisherman owe at the end of the first 7 years?b. what were his monthly repayments for remaining 18 years?c. how much interests in total did the fisherman pay at the end of the 25 years long.

Accepted Solution

A:

Amount borrowed, A1 = 85,000

Rate, i, for the first 7 years = 13.5% = 0.135

Rate, i, for the remaining 18 years = 15% = 0.15

Part (a): Amount owed after 7 years

Without interest rate, monthly payment, Po= 85,000/(12*25) = 283.33

After 7 years, principal amount remaining = 85,000 - (283.33*7*12) = 61,200.

Therefore, the amount owed after 7 years, A2 = 61,200

Part (b): Monthly repayment for the rest of 18 years

Rate, i = 15% = 0.15

Monthly payment, P(18) = A1*D2

D2 = {0.15/12}/{1-(1+0.15/12)^-12*25} = 0.01281

Then,

P(18) = 85,000*0.01281 = 1088.71

Part (c): Total interest paid

I =[ I(7) + I(18)] - A1

I(7) = P(7)*7*12 + P(18)*18*12

Now, P(7) = A1*D1

D1 = {0.135/12}/{1-(1+0.115/12)^-12*25} = 0.01165

Then,

P(7) = 85,000*0.01165 = 990.25

Therefore,

I = [990.25*7*12 + 1088.71*18*12] -85,000 = 318,341.50 -85,000 = 233,341.50

Rate, i, for the first 7 years = 13.5% = 0.135

Rate, i, for the remaining 18 years = 15% = 0.15

Part (a): Amount owed after 7 years

Without interest rate, monthly payment, Po= 85,000/(12*25) = 283.33

After 7 years, principal amount remaining = 85,000 - (283.33*7*12) = 61,200.

Therefore, the amount owed after 7 years, A2 = 61,200

Part (b): Monthly repayment for the rest of 18 years

Rate, i = 15% = 0.15

Monthly payment, P(18) = A1*D2

D2 = {0.15/12}/{1-(1+0.15/12)^-12*25} = 0.01281

Then,

P(18) = 85,000*0.01281 = 1088.71

Part (c): Total interest paid

I =[ I(7) + I(18)] - A1

I(7) = P(7)*7*12 + P(18)*18*12

Now, P(7) = A1*D1

D1 = {0.135/12}/{1-(1+0.115/12)^-12*25} = 0.01165

Then,

P(7) = 85,000*0.01165 = 990.25

Therefore,

I = [990.25*7*12 + 1088.71*18*12] -85,000 = 318,341.50 -85,000 = 233,341.50