Answer:
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total cost of the loan at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount taken as loan.
Considering bank A's offer
From the information given,
P = $15500
r = 6% = 6/100 = 0.06
n = 12 because it was compounded 12 times in a year.
t = 8 years
Therefore,
A = 15500(1 + 0.06/12)^12 × 8
A = 15500(1 + 0.005)^96
A = 15500(1.005)^96
A = $25019.2
The interest paid is
25019.2 - 15500 = $9519.2
Considering bank B's offer
From the information given,
P = $15500
r = 6.5% = 6.5/100 = 0.065
n = 12 because it was compounded 12 times in a year.
t = 7 years
Therefore,
A = 15500(1 + 0.065/12)^12 × 7
A = 15500(1 + 0.0054)^84
A = 15500(1.0054)^84
A = $24366
The interest paid is
24366 - 15500 = $8866
The interest that would by paid on bank B's offer is lower than that of bank A and the duration of the loan offer from bank B is shorter than that of bank A.
Therefore,
Bank A gives you more time to pay up the loan and you end up paying more interest
Bank gives you lesser time to pay up the loan and you end up paying lesser interest.
