7. suppose your savings account earns interest at an apr of 2.3% where interest is compounded annually. if…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula when compounded annually is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. Given $P=$250$, $r = 0.023$ (since $2.3%=0.023$).

Step2: Calculate the amount after 7 years

Substitute $P = 250$, $r=0.023$, and $t = 7$ into the formula: $A_1=250\times(1 + 0.023)^7$ $A_1=250\times(1.023)^7$ $(1.023)^7\approx1.175777$ $A_1=250\times1.175777\approx293.94$

Step3: Calculate the amount after 7.5 years

For 7.5 years, we first calculate the amount after 7 years using the compound - interest formula, and then calculate the simple interest for the remaining half - year. The amount after 7 years is $A_7 = 250\times(1.023)^7\approx293.94$. The simple - interest formula for half a year is $I=A_7\times r\times0.5$. $I = 293.94\times0.023\times0.5$ $I=293.94\times0.0115\approx3.38$ The amount after 7.5 years is $A_2=A_7 + I$ $A_2=293.94+3.38 = 297.32$

Answer:

The account is worth approximately $$293.94$ after 7 years and $$297.32$ after 7.5 years.