Final answer:
To cover Morgan's rent for five years at $850 per month with a 2.50% interest rate compounded monthly, Morgan's dad would need to invest approximately $48,388.47 today.
Step-by-step explanation:
Calculation of Present Value for a Savings Account with Monthly Compounded Interest
To calculate how much Morgan's dad should invest into a savings account to cover Morgan's rent for the next five years with rent at $850 per month and an interest rate of 2.50% compounded monthly, we can use the formula for the present value of an annuity. Since the rent is paid at the beginning of each month, we are dealing with an annuity due. The formula for the present value of an annuity due is PV = Pmt * [(1 - (1 + r)^(-nt)) / r] * (1+r), where Pmt is the monthly payment, r is the monthly interest rate, nt is the total number of compounding periods, and PV is the present value we want to find.
First, we calculate the monthly interest rate, which is the annual rate divided by 12:
r = annual interest rate / 12
r = 2.50% / 12
r = 0.0208333%
Next, we determine the total number of compounding periods of 5 years:
nt = number of years * number of compounding periods per year
nt = 5 * 12
nt = 60
Now, we can plug these values into the formula for the present value of an annuity due:
PV = 850 * [(1 - (1 + 0.0208333%)^(-60)) / 0.0208333%] * (1+0.0208333%)
After calculating, Morgan's dad would have to invest approximately $48,388.47 today to cover the rent for the next five years.