an investor deposited money into an investment account that earns interest compounded annually. the function…
an investor deposited money into an investment account that earns interest compounded annually. the function shown models the amount of money in the account in dollars after t years. a(t)=1,550(1.02)^t which statement best interprets one value in the function? a the initial deposit in the investment account was $1,581. b the amount of money in the investment account increases 102% each year. c the initial deposit in the investment account was $1,550. d the amount of money in the investment account decreases 2% each year.
Answer
Explanation:
Step1: Recall compound - interest formula
The compound - interest formula is $A(t)=P(1 + r)^t$, where $P$ is the principal (initial deposit), $r$ is the annual interest rate as a decimal, and $t$ is the number of years.
Step2: Identify values in given function
In the function $A(t)=1550(1.02)^t$, comparing with $A(t)=P(1 + r)^t$, we have $P = 1550$ (the initial deposit) and $r=0.02$ (2% interest rate). The value $1.02$ means the amount of money in the account increases by 2% each year since $1 + r=1+0.02 = 1.02$.
Answer:
D. The initial deposit in the investment account was $1,550.