Your cousin has just won the lottery and wants to create an account that will have $100,000 in 16 years to help pay for their child's college tuition. If the account has a fixed interest rate of 4.6% compounded 4 times each year, how much money should they put into the account?
Interest is compounded 64 times at
1.0115 times the previous balance.
X*(1 + 0.046/4)^64 = 100,000
X*2.0788195= 100,000
X = $48,104.22
To calculate the amount of money your cousin should put into the account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, in this case $100,000
P = the principal amount (initial investment/loan amount), what your cousin needs to figure out
r = annual interest rate (as a decimal), 4.6% or 0.046
n = number of times the interest is compounded per year, 4
t = number of years, 16
Let's plug in the given values into the formula and solve for P:
100,000 = P(1 + 0.046/4)^(4 * 16)
To find P, we need to isolate it on one side of the equation. Let's divide both sides of the equation by (1 + 0.046/4)^(4 * 16):
P = 100,000 / (1 + 0.046/4)^(4 * 16)
Using a calculator, evaluate the right side of the equation to find the value of P. The result will be the amount of money your cousin should put into the account to have $100,000 in 16 years.