Suppose that \( \$ 15,684 \) is invested at an interest rate of \( 6.8 \% \) per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time \( t \), in years. b) What is the balance after 1 year? 2 years? 5 years? 10 years? c) What is the doubling time? a) The exponential growth function is \( P(t)=15684 e^{0.068 t} \) (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.) b) The balance after 1 year is \( \$ 16,787.61 \). (Simplify your answers. Round to two decimal places as needed.) The balance after 2 years is \( \$ \square \). (Simplify your answers. Round to two decimal places as needed.)

The original price of a tablet was \( \$ 550 \). During a sale, Melvin was given a 30\% discount for the tablet. How much did he pay for the tablet?

You deposit \( \$ 1000 \) each year into an account earning \( 7 \% \) interest compounded annually. How much will you have in the account in 35 years?

"In addition, she said banks operating in Africa need to have a more end-to-end approach to risk management, considering bankability at all stages." As a followe up to Question 1 above and in addition to the solutions recommended in the anticle, recornmend how Southern African financial institutions can improve their risk management strategy.

Phil is shopping for an annuity that guarantees he CANNOT outlive the benefits. Which of these benefit options would he choose?Accelerated lifetime benefitGuaranteed lifetime withdrawal benefitRight of income riderGuaranteed minimum accumulation benefit

How much would you need to deposit in an account now in order to have \( \$ 3000 \) in the account in 15 years? Assume the account earns \( 5 \% \) interest compounded monthly.