Final answer:
To have $700 in 2 years at a 15% annual compound interest rate, Polly needs to deposit approximately $529.12 as the principal today.
Step-by-step explanation:
Calculating Initial Deposit with Compound Interest
To determine how much Polly needs to deposit today to have $700 in two years with an annual compound interest rate of 15%, we can use the formula for compound interest. The formula 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 (the initial amount of money), 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 or borrowed for, in years.
In Polly's case, since the interest is compounded annually, n is 1. Thus, the formula simplifies to A = P(1 + r)t. We want to find P, the principal, which is the amount Polly needs to deposit now. We know that A, the amount Polly wants after 2 years, is $700, r is 15% or 0.15 as a decimal, and t is 2 years.
To find P, we rearrange the formula to P = A / (1 + r)t. Substituting the given values, we get P = $700 / (1 + 0.15)2. Calculating this, P = $700 / (1.15)2 = $700 / 1.3225 = approximately $529.12.
Therefore, Polly needs to deposit $529.12 as the principal in her savings account to have $700.00 in two years at an interest rate of 15% compounded annually.