$800,000 if your rate of return is 5.3% compounded monthly
If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?
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Is $800,000 the future value in 20 years?
P(1+r)^20 = P(1+r)^10 * (1+r)^10
So, the amount after 10 years is
800000/(1+.053/12)^(12*10) = 471433.81
Your answer is wrong the correct answer is $296,631.79
To find out how much your savings will be worth after 10 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (the initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the initial deposit (P) is $800,000, the annual interest rate (r) is 5.3% or 0.053 in decimal form, and the rate is compounded monthly, so we compound interest 12 times per year (n = 12). We want to find the future value after 10 years, so t = 10.
Plugging these values into the formula, we have:
A = 800,000(1 + 0.053/12)^(12*10)
Calculating the value inside the parentheses first: (1 + 0.053/12)^(12*10) ≈ 1.55156112.
Now, we can substitute this value into the formula:
A = 800,000 * 1.55156112
Calculating A gives us:
A ≈ $1,241,248
Therefore, after 10 years, your savings will be worth approximately $1,241,248.