mario invested $6,000 in an account that pays 5% annual interest compounded annually. using the formula a =…

mario invested $6,000 in an account that pays 5% annual interest compounded annually. using the formula a = p(1 + r)^t, what is the approximate value of the account after 2.5 years? $6,075 $6,118 $6,456 $6,778

mario invested $6,000 in an account that pays 5% annual interest compounded annually. using the formula a = p(1 + r)^t, what is the approximate value of the account after 2.5 years? $6,075 $6,118 $6,456 $6,778

Answer

Explanation:

Step1: Identify the values

Given ( P = 6000), ( r=0.05), ( t = 2.5)

Step2: Substitute into the formula

Use the compound - interest formula ( A=P(1 + r)^{t}). Substitute the values: ( A = 6000\times(1+0.05)^{2.5})

Step3: Calculate ((1 + 0.05)^{2.5})

First, (1+0.05=1.05). Then, (1.05^{2.5}=e^{2.5\ln(1.05)}) (using the property (a^{b}=e^{b\ln(a)})). (\ln(1.05)\approx0.04879), so (2.5\times\ln(1.05)=2.5\times0.04879 = 0.121975). (e^{0.121975}\approx1.1293)

Step4: Calculate (A)

(A = 6000\times1.1293=6775.8\approx6778)

Answer:

($6,778)