Question 1090115
The compound interest formula is:
{{{A = P(1 + (r/n))^(nt)}}}
Where A is the final amount, P is the principal amount, r is the rate in decimal form, n is the number of times per year the interest is compounded, and t is the number of years.
So in part a), we have r = 0.08, n = 1, t = 5, and we want A to be 6000 since that is the desired amount at the end of the 5 years. So we need to solve for P.
{{{6000 = P(1 + (0.08/1))^(1*5)}}}
{{{6000 = P(1.08)^5}}}
{{{P = 4083.50}}}
Note that we round to two decimal places since this is money.  So if you want $6,000 at the end of 5 years, you need to start with $4,083.50.
For part b), the $15,000 is our P, our initial amount.  And t is 4.  So we are solving for A.
{{{A = 15000(1 + (0.08/1))^(1*4)}}}
{{{A = 15000(1.08)^4}}}
{{{A = 20407.33}}}
So at the end of 4 years, you will have to repay $20,407.33.