Question

What is the required annual interest rate to the nearest tenth of a percent for $5000 to grow to $6200 if interest is compounded quarterly for 8 years.?

Answer 1

About 2.7% annually

Explanation:

The equation for compound interest is `A=Pe^(rt)`
`A` is the end number, `P` is the initial price, `e` is a constant, `r` is the rate of change, and `t` is the times it is compounded

Plug it in:
`A=Pe^(rt)`
`6200=5000e^(r(32))`
`6200/5000=e^(r(32))`
`1.24=e^(r(32))`
`log_e(1.24)=r(32)`
`.21511137=r(32)`
`.21511137/32=r`
`r=.00672223`
`r=.672223%`

The rate quarterly is about .7%

The rate yearly is
`.672223(4)`
`2.688892`

About 2.7%

Plug it back in to check:
`6200=5000e^((.02688892/(4))(32))`
`6200=5000e^((.00672223)(32))`
`6200=5000e^(.21511136)`
`6200=5000(1.23999997)`
`6200=6200`