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Darlene Fine wants to have at least $50,000 in her savings account in 10 years. If her account pays 3.6% interest compounded annually, what should Darlene's initial investment be if she plans to keep the account without making deposits or withdrawals?

Verified Answer :

duskowl45

The formula for interest compounded annually is A=P(1+(r/n)^nt.
In this context: A=50,000     r=0.036    n=1, since it's compounded annually (Once per year) and t=10.

Now plug in and solve for P.
50,000=P(1+(0.036/1)^(1 * 10)
50,000= 1.42 P (I just distributed).
Divide both sides by 1.42 to get a final answer of $35,105.28.

Answer:   $ 35105.281

Step-by-step explanation:

Here the total amount after 10 years, A= $ 50,000

Annual interest rate, r = 3.6 %

Total number of years, t = 10 years.

Let P is the principal amount.

Then, \(A = P(1+\frac{r}{100} )^t\)

⇒ \(50,000 = P(1+\frac{3.6}{100} )^{10}\)

⇒  \(log(50,000) = log P+ 10 log(1+\frac{3.6}{100} )\)

⇒ P = 35105.281

Thus, the principal amount or initial investment = $ 35105.281


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