Question

$780 is invested in an account earning 9.9% interest (APR), compounded monthly. Write a function showing the value of the account after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.

Answer 1

Given :

The investment amount in account = $ 780

The rate of interest = r = 9.9% compounded monthly

The time period = t years

To Find :

A function showing the value of the account after t years

Solution :

From compound interest , compounded monthly

Amount = Principal × $( 1 +\dfrac{rate}{12 \times 100} )^{12 \times time}$

              = $ 780 × $( 1 +\dfrac{9.9}{12 \times 100} )^{12 \times t}$

              = $ 780 × $( 1 +\dfrac{9.9}{1200} )^{12t}$

              = $ 780 × $( 1.00825)^{12t}$

So, The function of account after t years =  $ 780 × $( 1.00825)^{12t}$

Hence, The function for annual growth after t years is  $ 780 $( 1.00825)^{12t}$ . Answer