Isabelle is considering whether it would be greatly beneficial for her to invest her money now rather than $5$5 years down the track. For an initial investment of $\$3000$$3000, the function $A=3000\left(1.026\right)^t$A=3000(1.026)t models how value her money will grow to in $t$t years.
Regardless of whether she invests now or in $5$5 years time, she will close the account when she retires (more than $8$8 years in the future).
How many times more will her closing balance be if she starts investing now rather than $5$5 years down the track? Give your answer correct to two decimal places.
At what annual compound interest rate, $r$r, must Joanne invest $\$220$$220 if she wishes to triple her money in $17$17 years? Give your answer as a percentage correct to two decimal places.
At what annual compound interest rate, $r$r, must you invest your money so that $\$1000$$1000 grows twofold in $16$16 years? Give your answer as a percentage, correct to 2 decimal places.
Find the principal, $P$P, that would need to be invested at $6%$6% p.a. compounded semiannually to accumulate $\$7600$$7600 in $9$9 years. Give your answer to the nearest dollar.