clarence has $20, 000 in the bank. He wants to create an investment to pay his $230 monthly car insurance payment for four years, with the first payment dude in one month. How much of his $20, 000 should he invest now at %8.25 per annum, compounded monthly?
230/mo * 48mo = 11040 = amt. to be
saved inc. interest.
n = 48 = the number of compounding
periods.
r = (8.25/12) /100 = 0.006875 = MPR =
Monthly percentage rate.
Po = 10^X.
X = log(Pt)-n*log(r+1)
X = log(11040) - 48*log(1.006875) =
X = 4.043 - 0.1428 = 3.900.
Po = 10^X = 10^3.90 = 7945.89 =
Initial investment.
To calculate how much Clarence should invest, we can use the formula for the future value of an investment with compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value of the investment
P is the principal amount (the initial investment)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In this case, Clarence wants to create an investment to cover his car insurance payment for four years. Since the payments are monthly, the interest should be compounded monthly. Therefore, we have:
A = $230 per month
P = amount to be determined
r = 8.25% per annum (or 0.0825 as a decimal)
n = 12 (since the interest is compounded monthly)
t = 4 years
Now, let's plug in these values and solve for P:
$230 = P(1 + 0.0825/12)^(12*4)
To find the value for P, we need to isolate it on one side of the equation:
P = $230 / (1 + 0.0825/12)^(12*4)
P ≈ $15,352.00
Therefore, Clarence should invest approximately $15,352.00 from his $20,000 to cover his car insurance payments for four years at an interest rate of 8.25% per annum, compounded monthly.