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you need to have $25,000 for a down payment on a house in 7 years. if you can earn an annual interest rate of 3.5 percent, how much will you have to deposit today?

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Final answer:

To have $25,000 in 7 years with an annual interest rate of 3.5 percent, one would need to deposit approximately $19,310.98 today. The calculation is based on the compound interest formula, adjusting for the given interest rate and time period.

Step-by-step explanation:

The question asks how much money you would need to deposit today to have $25,000 in 7 years if the account offers a 3.5 percent annual interest rate. To solve this, we use the formula for compound interest which is A = P(1 + r/n)nt, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

In the case where interest is compounded annually (n=1) and we want to find the initial deposit (P), the formula rearranges to P = A / (1 + r)t. Since we know A = $25,000, r = 3.5% or 0.035, and t = 7 years, we can calculate:

P = $25,000 / (1 + 0.035)7

Calculating this, the initial deposit P ≈ $19,310.98, which is the amount that needs to be deposited today to have $25,000 in 7 years at an annual interest rate of 3.5 percent.

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