Lucas wins $50,000(after taxes) in the lottery and decides to invest half of it in a 5-year CD that pays 5.35 percent compounded quarterly (4 times/year). He invests the other half in a money market fund that unfortunately turns out to average only 2.6 percent interest compunded annualy over the 5-year period. How much money will he have altogether in the two accounts at the end of the 5-year period?
P1 = Po(1+r)^n.
Po = $25,000.
r = (5.35%/4)/100% = 0.01338 = Quarterly % rate expressed as a decimal.
n = 4comp./yr. * 5yrs. = 20 Compounding
periods.
P2 = Po(1+r)^n.
r = 2.6%/100% = 0.026 = Annual % rate.
n = 1comp./yr. * 5yrs. = 5 Compounding
periods.
P1+P2 = Total Amt.
To calculate the final amount Lucas will have in the two accounts at the end of the 5-year period, we need to calculate the amount in each account separately and then add them together.
Let's start with the amount in the CD (Certificate of Deposit) account. Lucas invests half of $50,000, which is $25,000. The formula to calculate the future value of a CD investment is:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (to be calculated)
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, the principal (P) is $25,000, the annual interest rate (r) is 5.35% (or 0.0535 as a decimal), the interest is compounded quarterly (n = 4), and the investment period is 5 years (t = 5).
Using the formula, we can calculate the future value (A) of the CD investment:
A = $25,000(1 + 0.0535/4)^(4*5)
Now, let's calculate the amount in the money market fund. Lucas invests the other half of $50,000, which is also $25,000. The formula to calculate the future value of an investment with annual compounding is:
A = P(1 + r)^t
Where the variables have the same meanings as in the CD calculation. In this case, the principal (P) is $25,000, the annual interest rate (r) is 2.6% (or 0.026 as a decimal), and the investment period is 5 years (t = 5).
Using the formula, we can calculate the future value (A) of the money market fund investment:
A = $25,000(1 + 0.026)^5
Once we have calculated both amounts, we can add them together to find the total amount Lucas will have at the end of the 5-year period.