Question

$320 is invested in an account earning 8.1% interest (APR), compounded quarterly. 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

Explanation:

Given that:

The investment amount in account = $ 320

The rate of interest is = 8.1% compounded quarterly

Compunded quarterly means 8.1% / 4 = 0.02025

The time period = t years

The objective is to write a function showing the value of the account after t years.

From compound interest , compounded monthly.

`Amount = Principal * ( 1 + (rate)/(12*100))^(12*time)`

`= $320 *(1 + (0.02025)/(12*100))^(12t)`

`= 320*(1+ 1.6875*10^(-5))^(12t)`

`= 320 * ( 1.000016875)^(12t)`

Thus; the function after t years
`= $320 * ( 1.000016875)^(12t)`

The percentage of growth per year is :

= (1 + 0.02025)^4 - 1

= 1.083493758 - 1

= 0.083493758

= 8.4 % (APY) yearly