You think that you will be able to deposits ￡4000 at the end of each of the next three years in a bank account paying 8 percent interest. You currently have ￡7000 in the account? How much will you have in three years? In four years?

To solve this problem, we need to calculate the future value of the deposits and the current balance in the account after three and four years.<br /><br />Given information:<br />- Deposits: $￡4000$ at the end of each year for the next three years<br />- Interest rate: 8% per annum<br />- Current balance: $￡7000$<br /><br />Step 1: Calculate the future value of the deposits after three years.<br />The formula for the future value of an ordinary annuity is:<br />FV = P × [(1 + r)^n - 1] / r<br /><br />Where:<br />FV = Future value<br />P = Periodic payment (deposit)<br />r = Interest rate per period<br />n = Number of periods<br /><br />FV = $4000 × [(1 + 0.08)^3 - 1] / 0.08<br />FV = $4000 × [1.2597 - 1] / 0.08<br />FV = $4000 × 0.2597 / 0.08<br />FV = $12,925<br /><br />Step 2: Calculate the future value of the current balance after three years.<br />FV = PV × (1 + r)^n<br /><br />Where:<br />FV = Future value<br />PV = Present value (current balance)<br />r = Interest rate per period<br />n = Number of periods<br /><br />FV = $7000 × (1 + 0.08)^3<br />FV = $7000 × 1.2597<br />FV = $8,814.90<br /><br />Step 3: Calculate the total amount after three years.<br />Total amount = Future value of deposits + Future value of current balance<br />Total amount = $12,925 + $8,814.90<br />Total amount = $21,739.90<br /><br />Step 4: Calculate the future value of the deposits after four years.<br />FV = $4000 × [(1 + 0.08)^4 - 1] / 0.08<br />FV = $4000 × [1.3605 - 1] / 0.08<br />FV = $4000 × 0.3605 / 0.08<br />FV = $18,025<br /><br />Step 5: Calculate the future value of the current balance after four years.<br />FV = $7000 × (1 + 0.08)^4<br />FV = $7000 × 1.3605<br />FV = $9,542.50<br /><br />Step 6: Calculate the total amount after four years.<br />Total amount = Future value of deposits + Future value of current balance<br />Total amount = $18,025 + $9,542.50<br />Total amount = $27,567.50<br /><br />Therefore, the amount in the account after three years will be $21,739.90, and the amount in the account after four years will be $27,567.50.