Future value and simple interest On a loan of $3,000 at an interest rate of 12% per year when half of the loan principal is repaid as a lump sum at the end of four years and the other half is repaid in one lump sum amount at the end of eight years, and if the interest is not paid each year but added to the outstanding principal plus accumulated interest, how much interest will be due to the lender as a lump sum at the end of the eighth year? My Approach: F = P(1+i)^n = 1500(1+0.12)^4 I = PNi = 3000x4x0.12 adding them together gives me $3800.28 But this answer is not in my multiple choices

Easiest, I think, is to break it into two loans (both at $12\%$):

Loan $1$: borrow $1500$ for $8$ years, financing the interest. The total accumulated debt is then $$1500\times 1.12^8=3713.94$$

Of that, $1500$ is principle so this loan represents interest of $\fbox {2213.94}$

Loan $2$: borrow $\$1500$ for $4$ years (financing the interest payments). Pay the principle back at the end of the $4$ years BUT keep financing the interest for another $4$ years. We compute $$1500\times 1.12^4=2360.28$$ so when we repay the $1500$ we still have the accumulated interest of $860.28$. Of course we are still financing that so, four years later that interest has grown to $$860.28\times 1.12^4=\fbox {1353.67}$$

The final answer is the sum: $$2213.94+1353.67 = \fbox {3567.61}$$