Respuesta :
Answer:
$19,107.48
Explanation:
Data provided in the question:
Total time = 5 years
Initial deposit = $10,000
Interest rate for the first 3 years = 12% compounded monthly
Interest rate for the last 2 years = 15% compounded semiannually
Now,
Amount after 3 years = [tex]P \times( 1 + \frac{r}{n})^{\Large{n \times t}}[/tex]
Here,
P = Amount of money deposited,
r = annual interest rate
n = number of times compounded per year = 12 for monthly compounding
t = time in years
Thus,
Amount after 3 years = 10000 [tex]\times( 1 + \frac{ 0.12 }{ 12 } \right)^{\Large{ 12 \times3 }}[/tex]
= 10000 × 1.1³⁶
= $14,307.69
Therefore,
Deposit for last 2 years = $14,307.69
Thus,
Final amount after 2 years with deposit of $14,307.69
= 14307.69 × [tex]\left( 1 + \frac{ 0.15 }{ 2 } \right)^{\Large{ 2 \times2 }}[/tex]
= 14307.69 × 1.075⁴
= 14307.69 × 1.335469
= $19,107.48
Hence,
The final amount after 5 years = $19,107.48
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