Question

Yael has $3,000 to invest. She wants to split the money equally between an account that

pays four percent interest with a five-year investment term and an account with a two
percent interest rate with an eight-year investment term.
Use the time value of money formula [(1+r) i.e. for 3 %=.03 interest for 2 years = 1.03²]
to figure out how much money each account would be worth when she's able to
withdraw the money. Which account is worth more?

Answer 1

so she's evenly splitting it into $1500 and $1500.

how much will it be for $1500 at 4% APR for 5 years?

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1500\\ r=rate\to 4\%\to (4)/(100)\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 1500\left(1+(0.04)/(1)\right)^(1\cdot 5) \implies A = 1500( 1.04)^(5)\implies \boxed{A \approx 1824.98}`

now how much will it be for $1500 with a 2% APR for 8 years?

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1500\\ r=rate\to 2\%\to (2)/(100)\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &8 \end{cases} \\\\\\ A = 1500\left(1+(0.02)/(1)\right)^(1\cdot 8) \implies A = 1500( 1.02)^(8)\implies \boxed{A \approx 1757.49}`

well, clearly
`{\Large \begin{array}{llll} 1824.98 ~~ > ~~ 1757.49 \end{array}}`