Your aunt places $$13,000$ into an account earning an interest rate of $7\%$ per year. After five years the account will be valued at $$18,233\mathrm{.}17.$ Which of the following statements is correct?

Question $17$ options:

a$)$

The present value is $$13,000,$ the time period is $7$ years, the present value is $$18,233\mathrm{.}17,$ and the interest rate is $5\%.$

b$)$

The future value is $$13,000,$ the time period is $5$ years, the principal is $$18,233\mathrm{.}17,$ and the interest rate is $7\%.$

c$)$

The principal is $$13,000,$ the time period is $5$ years, the future value is $$18,233\mathrm{.}17,$ and the interest rate is $7\%.$

d$)$

The principal is $$13,000,$ the time period is $7$ years, the future value is $$18,233\mathrm{.}17,$ and the interest rate is $5\%.$