Question

Determine the amount of money accumulated in 5 years with an initial deposit of $10,000, if the account earned 12% compounded monthly the first 3 years and 15% compounded semiannually the last 2 years.

Answer 1

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 = $P \times( 1 + \frac{r}{n})^{\Large{n \times t}}$

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 $\times( 1 + \frac{ 0.12 }{ 12 } \right)^{\Large{ 12 \times3 }}$

= 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 × $\left( 1 + \frac{ 0.15 }{ 2 } \right)^{\Large{ 2 \times2 }}$

= 14307.69 × 1.075⁴

= 14307.69  × 1.335469

= $19,107.48

Hence,

The final amount after 5 years = $19,107.48