Question

hmed has 40000 EgyptianPounds to invest. He wantsto split his money equallybetween a savings account withsimple interest rate of 1.2% paid annually and a two-yearguaranteed investment certificates(GIC) with an interest rate of 3.5%, compounded monthly.How long will he have to leavethe money in the savings accountso that it earns the same amountas the GIC?

Answer 1

`\begin{gathered} Total=40000 \\ For\text{ saving account} \\ P=20000 \\ i=1.2\text{ \%= 0.012 }simple\text{ interest annually} \\ \text{For }GIC \\ P=20000 \\ i=3.5\text{ \% = 0.035 compounded monthly } \\ t=\text{ }2\text{ years = 24 months} \\ To\text{ find the earning in GIC} \\ F=P(1+i)^t \\ F=20000(1+0.035)^(24) \\ F=20000(1.035)^(24) \\ F=45666.6 \\ \text{ earning = 45666.6-20000} \\ \text{ earning = 25666.6} \\ \text{The earning is 25666.6} \\ To\text{ find the time in }simple\text{ interest annually} \\ \text{earning = P}\cdot i\cdot t \\ \text{Solving t} \\ t=\frac{\text{earning}}{P\cdot i} \\ t=(25666.6)/((20000)(0.012)) \\ t=106.9=107\text{ years} \\ \text{The time in }simple\text{ interest account to get the same earning as GIC is 107 years} \end{gathered}`