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Sarah borrowed $100,000 at 8% for 10 years on January 1, 2020 from a local bank

Finance Nov 27, 2020

Sarah borrowed $100,000 at 8% for 10 years on January 1, 2020 from a local bank. The loan is supposed to be paid back interest only for the first 5 years and principal and interest together starting beginning year six. The loan will be paid off on December 31, 2030. How much total interest she will pay at the end of year 2030?

Expert Solution

 

The initial loan was taken for 100,000

For the first 5 yrs , the loan has been paid back the interest only

So the Interest for each year = 100,000 * 8% = 8000 per year

Total interest for 5 Year (INTEREST 1) = 5 * 8000 = 40,000

Now the loan is amortized for both principal and interest for the remaining 5 years

So the

Amortization payments

payment = P*(i)   / ( 1- (1+i) ^–t

Where p = principal

I = interest rate

T = time

payment = P*(i/m)   / ( 1- (1+i/m) ^–mt   = 100,000 *(0.08) /1-(1+0.08)^-5 = 25,045.65

So the Yearly payment are = $ 25,045.65

Total instalment paid on the loan = 25045.65 * 5 = 125,228.23

So the interest part is = 125,228.23 – 100,000 = 25,228.23

Hence to total interest paid is = Lat 5 yrs interest + First 5 yrs interest = 25,228.23 + 40,000 = 65,228.23

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