Question

Tim invests $1000 in an annuity that offers an interest rate of 3.5% compound quarterly for 5 years. What is the value of Tim's investment after 5 years

Answer 1

Answer:$1190.34 baby

Explanation:

Answer 2

The formula we will use is
`A(t)=P(1+ (r)/(n))^{(n)(t)`, where A(t) is the amount we have at the end of the time, P is the initial investment amount, n is the number of times the money is compounded, r is the interest rate in decimal form, and t is the number of years we are investing. For us, P=1000, r=.035, n = 4 (quarterly is 4 times a year), and t = 5. Filling in accordingly, we have
`A(t)=1000(1+ (.035)/(4))^{(4)(5)`. Simplifying within the parenthesis we have
`A(t)=1000(1+.00875)^(20)`. Again simplfiying,
`A(t)=1000(1.00875)^(20)`. Raise the parenthesis to the power of 20 to get A(t) = 1000(1.190339799). Now we can multiply to find the amount at the end of it all. A(t) = $1,190.34