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Let's calculate the amounts Jenny and Frank will have after one year with their respective accounts, considering Jenny's account has simple interest and Frank's account has compound interest.
Jenny's Account (Simple Interest):
- Principal (P) = $50,000
- Rate of interest (r) = 4%
- Time (t) = 1 year
The formula for simple interest is:
[tex]\text{Simple Interest (SI)} = P \times r \times t[/tex]
Calculate Jenny's interest:
[tex]\text{SI} = 50000 \times 0.04 \times 1 = 2000[/tex]
Amount after one year:
[tex]\text{Total amount} = P + \text{SI} = 50000 + 2000 = 52000[/tex]
Frank's Account (Compounded Annually):
- Principal (P) = $50,000
- Rate of interest (r) = 4%
- Time (t) = 1 year
The formula for compound interest annually is:
[tex]A = P \left(1 + r\right)^t[/tex]
Calculate Frank's amount:
[tex]A = 50000 \left(1 + 0.04\right)^1 \\\\ A = 50000 \times 1.04 \\\\ A = 52000[/tex]
Therefore, after one year:
- Jenny will have 52000 dollars.
- Frank will also have 52000 dollars.