Martina received a $1200 bonus. She decided to invest it in a 3-year certificate of deposit (CD) with an annual interest rate of 1.34% compounded daily

Break Down the Problem

1. Identify the principal amount (P), which is the initial investment: $1200.
2. Determine the annual interest rate (r): 1.34% (or 0.0134 as a decimal).
3. Determine the number of years (t): 3 years.
4. Identify the compounding frequency. Since it's compounded daily, we have: n = 365 days/year.

Relevant Concepts

The formula for compound interest is given by: $A = P \left(1 + \frac{r}{n}\right)^{nt}$ Where:

• $A$ = the amount of money accumulated after n years, including interest.
• $P$ = the principal amount (the initial amount of money).
• $r$ = the annual interest rate (decimal).
• $n$ = the number of times that interest is compounded per year.
• $t$ = the number of years.

Analysis and Detail

1. Substituting the known values:

   • $P = 1200$
   • $r = 0.0134$
   • $n = 365$
   • $t = 3$

   Plug these values into the compound interest formula: $A = 1200 \left(1 + \frac{0.0134}{365}\right)^{365 \cdot 3}$

2. Calculating the values in the formula:

   • Calculate $\frac{0.0134}{365}$: $\frac{0.0134}{365} \approx 0.000036707$
   • Now, calculate $n \cdot t = 365 \cdot 3 = 1095$.
   • Substitute back into the formula: $A \approx 1200 \left(1 + 0.000036707\right)^{1095}$

3. Calculate $A$:

   • First find $1 + 0.000036707$: $1 + 0.000036707 \approx 1.000036707$
   • Now raise this to the power of 1095: $(1.000036707)^{1095} \approx 1.041379$
   • Then multiply by the principal: $A \approx 1200 \times 1.041379 \approx 1249.65$

Verify and Summarize

1. Final amount after compounding is approximately $A = 1249.65$.
2. This means that after 3 years, Martina's investment will grow from $1200 to approximately$1249.65.

Final Answer

The amount accumulated after 3 years will be approximately $1249.65.