Question

1. 30-year, $100K loan @4% with monthly payments... How much interest will be paid in only the second year? LG puts 13=24 Int=43896
i have the answer im just not sure how we got this answer. can you explain how to solve it with finacial calulator.

Answer 1

Step 1: We can use PV of an Annuity formula to calculate the monthly payment of loan

PV = PMT * [1-(1+i) ^-n)]/i

Where PV = $100,000

PMT = Monthly payment =?

n = N = number of payments = 30 years *12 months =360 month

i = I/Y = interest rate per year = 4%, therefore monthly interest rate is 4%/12 = 0.33% per month

Therefore,

$100,000 = PMT* [1- (1+0.0033)^-360]/0.0033

PMT = $477.42

Monthly payment is $477.42

Step 2: Let’s calculate Outstanding balance on loan after 1 year of loan; it can be calculated by assuming PMT = Monthly payment =$477.42

n = N = number of payments = 29 years *12 months =348 months

Therefore,

Outstanding balance on loan after one year (PV1) = $477.42* [1- (1+0.0033)^-348]/0.0033

= $98,238.96

Step 3: Outstanding balance on loan after 2 year of loan; it can be calculated by assuming PMT = Monthly payment =$477.42

n = N = number of payments = 28 years *12 months =336 months

Therefore,

Outstanding balance on loan after two years (PV2) = $477.42* [1- (1+0.0033)^-336]/0.0033

= $96,406.18

Step 4: Now the interest will be paid in only the second year = Monthly payment for 12 months of second year – (Outstanding balance on loan after one year (PV1) - Outstanding balance on loan after two years (PV2))

= 12 * $477.42 – ($98,238.96 -$96,406.18)

= $5,728.98 - $1,832.78

= $3,896.20 or $3,896 (rounding off to nearest whole number)

Therefore the interest will be paid in only the second year is $3,896