$6.$ Finding the interest rate and the number of years

The future value and present value equations also help in finding the interest rate and the number of years that correspond to present and future value calculations.

If a security currently worth $$9,200$ will be worth $$15,767\mathrm{.}18$ seven years in the future, what is the implied interest rate the investor will earn on the security$$assuming that no additional deposits or withdrawals are made?

$1\mathrm{.}71\%$

$5\mathrm{.}83\%$

$8\mathrm{.}00\%$

$6\mathrm{.}40\%$

If an investment of $$50,000$ is earning an interest rate of $8\mathrm{.}00\%,$ compounded annually, then it will take for this investment to reach a value of $$89,052\mathrm{.}92$assuming that no additional deposits or withdrawals are made during this time.

Which of the following statements is true$$assuming that no additional deposits or withdrawals are made?

An investment of $$50$ at an annual rate of $5\%$ will return a higher value in five years than $$25$ invested at an annual rate of $10\%$ in the same time.

An investment of $$25$ at an annual rate of $10\%$ will return a higher value in five years than $$50$ invested at an annual rate of $5\%$ in the same time.