# Math

Serena wanst to borrow \$15 000 an pay it back in 10 years. Interest rates are so high, so the bank makes her 2 offers

option 1 - borrow the money at 12%/a compounded quarterly for the full term

option 2 -Borrow the money at 12%/a compunded quarterly for 5 years and then renegotiate the loan based on the mew balance for he last 5 years

if in 5 years the interest rate wil be 6%/a compunded quarterly , how much will Serena save by choosing the second option

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1. option 1
amount after 10 years = 15000(1.03)^40 = 48930.57

option 2
amount after 5 years at first rate = 15000(1.03)^20 = 27091.67
amount of that 5 years later at new rate
= 27091.67(1.015)^20 = 36488.55

take the difference

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