I need help the question is long.

Question

you deposit $450 into an investment account that earns 12% annual interest compounded quarterly. the graph shows the balance of a saving account over time. write that function that represents the balances of the accounts after t years. how much will be in the account after 10 years? Round to the nearest hundredth.

Answer 1

Hi, Niso.

This is a standard compound interest problem, where an amount, P (the principal) is deposited into an account and earns interest at a fixed rate per period.

The compound interest formula is: A = P (1 +i / 12)^12t

In the above equation, we divide the annual interest rate by 12 to get the monthly rate and multiply the period in years by 12 to get the number of monthly compounding periods.

Therefore, A = 450 (1 + 0.12/12)^12t

A = 450 (1.01)^12t <--- this is the required function

After 10 years, A = 450 x 1.01^12x10

= 450 x 1.01¹²⁰

= 450 x 3.30039

= $1,485.17 [this is the amount after 10 years or 120 months]