Posted by **Maame** on Sunday, May 20, 2012 at 4:59pm.

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 -
**Henry**, Monday, May 21, 2012 at 4:58pm
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.

## Answer this Question

## Related Questions

- Math - Serena wanst to borrow $15 000 an pay it back in 10 years. Interest rates...
- Mathematics and investment - 1. Angelo wants to renovate his house in 3 years. ...
- math - Jim wants to deposit money in an account to save for a new stereo system ...
- uno - You decide to borrow $200,000 to build a new house. The bank charges an ...
- fianance - 3. You decide to borrow $200,000 to build a new house. The bank ...
- finance - 3. You decide to borrow $200,000 to build a new house. The bank ...
- finance - 3. You decide to borrow $200,000 to build a new house. The bank ...
- math/ compounded - Scenario: A client comes to you for investment advice on his...
- math - Suppose you borrow $12,000, which you must pay back in 30 equal monthly ...
- Math - Mr. Nielson wants to borrow $1,000 for 2 years. He is given the choice of...