# Math

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Serena wants to borrow \$15 000 and pay it back in 10 years. Interest rates are
high, so the bank makes her two offers:
• Option 1: Borrow the money at 10%/a compounded quarterly for
the full term.
• Option 2: Borrow the money at 12%/a compounded quarterly for 5 years
and then renegotiate the loan based on the new balance for the last 5 years.
If, in 5 years, the interest rate will be 6%/a compounded quarterly, how
much will Serena save by choosing the second option?

steps and formula to get answer will be nice, so i know how it works

• Math -

Option !:

P = Po(1+r)^n.

r = (10%/4) / 100% = 0.025 = Quarterly
% rate expressed as a decimal.

n = 4Comp./yr * 10yrs = 40 Compounding
periods.

P = 15000(1.025)^40 = \$40,275.96

Int. = P - Po = 40275.96 - 15000 = 25,275.96.

Option 2:

P = 15000(1.03)^20 = \$27,091.67

P = 27091.67(1.015)^20 = \$36,488.55.

Int. = 36,488.55 - 15000 = \$21,488.55.

Saved = 25,275.96 - 21,488.55 = \$3787.41

NOTE: The procedure for calculating r is the same for both options.

• sex -

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