ceLab Assignment
Question 5, P5-14 (similar to)
HW Score: $26.62 \%, 13$.
Points: 0 of 3
(Related to Checkpoint 5.6) (Solving for I) At what annual interest rate, compounded annually, would $\$ 510$ have to be invested for it to grow to $\$ 1,995.04$ in 13 years?
The annual interest rate, compounded annually, at which $\$ 510$ must be invested for it to grow to $\$ 1,995.04$ in 13 years is $\square$ \%. (Round to two decimal places.)
Answer
The annual interest rate, compounded annually, at which \$510 must be invested for it to grow to \$1995.04 in 13 years is \(\boxed{11.06\%}\).
Step 1 ：Define the known values: \(A = \$1995.04\), \(P = \$510\), \(n = 1\), \(t = 13\).
Step 2 ：Calculate the annual interest rate \(r\) using the formula \((A/P)^{1/(n*t)} - 1) * n\).
Step 3 ：Substitute the known values into the formula to get \(r = ((1995.04/510)^{1/(1*13)} - 1) * 1 = 0.1106259136587473\).
Step 4 ：Convert \(r\) to a percentage by multiplying by 100 to get \(r_{\%} = 0.1106259136587473 * 100 = 11.06259136587473\% \).
Step 5 ：Round \(r_{\%}\) to two decimal places to get the final answer.
Step 6 ：The annual interest rate, compounded annually, at which \$510 must be invested for it to grow to \$1995.04 in 13 years is \(\boxed{11.06\%}\).
