You have just placed $1,500 in a bank savings deposit and plan to hold that
deposit for eight years, earning 5½ percent per annum. If the bank compounds interest daily, what will be the total value of the deposit in eight years? How does your answer change if the bank switches to monthly compounding? Quarterly compounding?
To calculate the total value of the deposit after eight years with daily compounding, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total value of the deposit
P = the principal amount (initial deposit)
r = annual interest rate (in decimal form; 5½ percent = 0.055)
n = number of times the interest is compounded per year
t = number of years
For daily compounding, n would be 365 (since there are 365 days in a year). Plugging in the values:
A = $1,500(1 + 0.055/365)^(365*8)
Calculating this using a calculator or a spreadsheet tool, we find that the total value of the deposit after eight years with daily compounding is approximately $2,062.32.
Now, let's calculate the total value of the deposit after eight years with monthly compounding. For monthly compounding, n would be 12 (since there are 12 months in a year). Plugging in the values:
A = $1,500(1 + 0.055/12)^(12*8)
Calculating this, we find that the total value of the deposit after eight years with monthly compounding is approximately $2,061.41.
Lastly, let's calculate the total value of the deposit after eight years with quarterly compounding. For quarterly compounding, n would be 4 (since there are 4 quarters in a year). Plugging in the values:
A = $1,500(1 + 0.055/4)^(4*8)
Calculating this, we find that the total value of the deposit after eight years with quarterly compounding is approximately $2,061.60.
So, as we can see, the total value of the deposit differs slightly depending on the compounding frequency. Daily compounding results in a slightly higher value compared to monthly and quarterly compounding, as the interest is compounded more frequently.