Answer :
The amounts in the bank after 7 years for each compounding period are: Annually compounded: $7926.64; Quarterly compounded: $7951.62; Monthly compounded: $7959.45; Continuously compounded: $7968.64.
To calculate the amount in the bank after 7 years with different compounding periods, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
For the first case, where interest is compounded annually:
P = $5000
r = 0.06 (6% as a decimal)
n = 1 (compounded annually)
t = 7
Substituting these values into the formula, we get:
A = 5000(1 + 0.06/1)^(1*7)
Calculating this, we find that the amount in the bank after 7 years with annual compounding is approximately $7926.64.
For the second case, where interest is compounded quarterly:
P = $5000
r = 0.06
n = 4 (compounded quarterly)
t = 7
Substituting these values into the formula:
A = 5000(1 + 0.06/4)^(4*7)
Calculating this, we find that the amount in the bank after 7 years with quarterly compounding is approximately $7951.62.
For the third case, where interest is compounded monthly:
P = $5000
r = 0.06
n = 12 (compounded monthly)
t = 7
Substituting these values into the formula:
A = 5000(1 + 0.06/12)^(12*7)
Calculating this, we find that the amount in the bank after 7 years with monthly compounding is approximately $7959.45.
Finally, for the case of continuous compounding:
P = $5000
r = 0.06
n = infinity (continuous compounding)
t = 7
Substituting these values into the formula:
A = 5000 * e^(0.06*7)
Calculating this, we find that the amount in the bank after 7 years with continuous compounding is approximately $7968.64.
To know more about compound interest:
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