Final answer:
For a 1-year investment, Option A yields more due to a slightly higher simple interest rate. However, over a period of 5 years, Option B is superior because compound interest leads to a higher total return. Thus, the best choice for Mark is Option A for 1 year and Option B for 5 years.
Step-by-step explanation:
Comparing Investment Options for Mark
To determine which investment option is better for Mark either for 1 year or 5 years, we need to calculate the total amount Mark will have after investing $50,000 in each option.
For Option A which pays 3.45% simple interest, the total interest for 1 year will be:
$50,000 × 0.0345 × 1 = $1,725
And for 5 years, the total interest with simple interest remains constant per year:
$50,000 × 0.0345 × 5 = $8,625
Thus, the total amount after 5 years with Option A will be:
$50,000 + $8,625 = $58,625
For Option B which offers 3.2% interest compounded annually, the formula for compound interest is used to calculate the total:
A = P(1 + r/n)^(nt)
For 1 year, the calculation would be:
$50,000(1 + 0.032)^1 = $51,600
And for 5 years, the calculation would be:
$50,000(1 + 0.032)^5 ≈ $58,963.59
Comparing the total amounts after 1 year and 5 years for both options:
- After 1 year: Option A gives $51,725, and Option B gives $51,600.
- After 5 years: Option A gives $58,625, and Option B gives approximately $58,963.59.
It can be concluded that:
- For 1 year, Option A is better because it yields a slightly higher amount.
- For 5 years, Option B is better due to the effect of compound interest.
Therefore, the correct choice is:
d) Option A for 1 year, Option B for 5 years