## Problem 2051

Suppose you borrow 560 for a term of five years at simple interest and 2.06% APR.

Determine the total (principal plus interest) you must pay back on the loan.

**Solution:-**

The future payoff, F, which is principal plus interest, obeys the formula F = P(1 + tr), where P is the principal, r is the APR expressed as a decimal, and t is term of the loan in years.

Since the formula requires that the interest rate be written as a decimal, begin by writing the APR of 2.06% as a decimal. To convert a percentage to a decimal, divide by 100.

2.06% = 0.0206

Identify P. Remember that P is the principal, or present value. It is the amount initially borrowed.

P = 560

Identify t. Remember that is the term of the loan in years.

t = 5

Now substitute 560 for P, 0.0206 for r, and 5 for t in formula.

F = P(1 + tr)

= 560 (1 + 0.0206*5)

617.68

Therefore, the total (principal plus interest ) you must pay back on the loan is 617.68.