Can you help me with this question?
this can be solved using present value of annuity formula
present value of annuity = PMT[1 - (1+r)-n / r]
where,PMT = monthly payments
r = rate of interest
n = number of periods
monthly payments:
option 1:
here interest rate = 8.15%
since monthly payments = 8.15 / 12 = 0.67917%
n = 30 x 12 = 360
40,000 = PMT[1 - (1.0067917)-12 x 30 / 0.0067917]
PMT = 40,000 / 134.3637884
monthly payments = $297.70
Option 2:
here interest rate = 7.75%
since monthly payments = 7.75 / 12 =0.645833%
n = 15 x 12 = 180
40,000 = PMT[1 - (1.00645833)^-180 / 0.00645833]
PMT = 40,000 / 106.2388
monthly payments = $376.51
Total payment for option 1 = 360 x 297.70 = $107,172
Total Payment for Option 2 = 180 x 376.51 = $67,771.85
when we compare both the options Option 2 is economically better because it has low interest rate even though Option 1 seems to be better option because of low monthly payments we end up being pay more interest.
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