Betsy inherits 1500 and would like to put some of it away for a down payment on a house in 8 years. if she would like to have 25000 for the down payment, how much of her inheritance must she invest at 9.2% a compounded quarterly
Please tell me where to invest at a 9.2% apr rate -- much less where it's compounded quarterly.
i don't know , but here is the question again.
Betsy inherits $15 000 and would like to put some of it away for a down
payment on a house in 8 years. If she would like to have $25 000 for the
down payment, how much of her inheritance must she invest at 9.2%/a
compounded quarterly?
To find out how much of Betsy's inheritance she must invest at 9.2% compounded quarterly to reach $25,000 in 8 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value (amount of money Betsy wants to have)
P = the principal (amount of money Betsy needs to invest)
r = the interest rate (9.2% or 0.092 as a decimal)
n = the number of times interest is compounded per year (4 times for quarterly compounding)
t = the number of years (8 years)
Substituting the given values into the formula, we have:
25000 = P(1 + 0.092/4)^(4*8)
Now we can solve for P:
25000 = P(1 + 0.023)^32
25000 = P(1.023)^32
25000 = P(1.93523)
P = 25000 / 1.93523
P ≈ 12914.43
Therefore, Betsy must invest approximately $12,914.43 of her inheritance at 9.2% compounded quarterly to have $25,000 for the down payment on a house in 8 years.