Suppose that $14,000 is invested in a savings account paying 5.2% interest per year.
(a) Write the formula for the amount A in the account after t years if interest is compounded monthly.
To find the formula for the amount A in the account after t years with monthly compounding interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount in the account after t years
P is the principal amount (initial investment) which is $14,000 in this case
r is the annual interest rate in decimal form, which is 0.052 (5.2% as a decimal)
n is the number of times the interest is compounded per year, which is 12 for monthly compounding
t is the number of years the money is invested, which is t in this case.
Plugging in the values into the formula, we get:
A = 14,000(1 + 0.052/12)^(12t)
This is the formula for the amount A in the account after t years with monthly compounding interest.
A = Po(1+r)^n.
Po = $14,000.
r = 0.052/12 = 0.0043/mo.
n = 12comp./yr. * t yrs. = 12t compounding periods.