Math Problem Help How Do You Do This

Suppose a $13262 loan has an annual compound interest rate of 5.7% with semi-annual compounding (twice per year). If the loan’s term is 8 years, what is its future value? 

Round your answer to the nearest dollar.

Solution

The loan is $13,262. Every 6 months the value of the loan increases by 0.057/2 = 0.0285 (2.85%).

At the end of the 1st 6 month period, the loan is worth $13,262 * (1+0.0285) = $13,639.97.

By the end of the first year, there have been 2 6-month periods when interest was paid in, so the value of the loan is $13,262 * (1+0.0285)*(1+0.0285) = $13,262 * (1.0285)2 = $14,028.71.

During 8 years, there are 16 6-month periods during which interest is accrued. Thus, the final value of the loan, to the nearest dollar, is 13,262 * (1.0285)16 = $20,791.