An investment of $$$$4445\mathrm{.}27$ earns interest at $8\mathrm{.}1\%$ per annum compounded monthly for $3$ years. At that time the interest rate is changed to $1\mathrm{.}3\%$ compounded semi dash annually. How much will the accumulated value be $1\mathrm{.}5$ years after the$$ change? For compound$$ interest, the formula for the future$$ value, FV$,$ is given$$ below, where PV is the original$$ principal, i is the periodic rate of$$ interest, and n is the number of compounding periods for the term of the loan or investment.

FVequalsPV left parenthesis $1$ plus i right parenthesis Superscript n

The periodic rate of$$ interest, i$,$ can be found using the formula shown$$ below, where j is the nominal annual rate of interest and m is the number of compounding$($conversion$)$ periods per year.

iequalsStartFraction j Over m EndFraction

Use the future value formula in two steps. Start by finding the future value at the end of the first time period.$$ Then, using that result as the present$$ value, find the future value at the end of the second time period.