Respuesta :
Answer: $3,527,337
Explanation:
Future value (FV) = $20 million
Interest rate (i) = 6% = 6/100 = 0.06
Time period (n) = 5 years
Then, the amount of the required annual deposit is calculated below:
Future value of the annuity (FV) = A × [(1+i)^n -1] × (1/i)
We then slot in the values and this will be:
20 million = A (1+6%)^5 - 1] × (1/6%)
20 million = A [(1+0.06)^5 - 1] × (1/0.06)
20 million = A [(1.06)^5 - 1] × (1/0.06)
20 million = A [1.34 - 1] × (1/0.06)
20 million = A [0.34] × (1/0.06)
20 million = A [0.34/0.06)
20 million = A × 5.67
A = 20 million / 5.67
A = 3527337.3
Therefore, required annual deposit = $3,527,337
The amount that is required to be paid as annual deposit is $3,344,481 as the first deposit is scheduled to be made on July 1, 2019.
What is the Future Value of annuity?
Future annuity value is the group of repeated payments for a specific future date, deducted a certain refund rate, or a discount rate. The higher the discount rate, the greater the annuity amount.
The formula for calculation for future annuity value:
[tex]FV(due) = A[\dfrac{(1+r)^{n} - 1} {r}](1 + r)[/tex]
We can use the future value of annuity formula to calculate the amount of the required annual deposit:
[tex]\rm\,Future\,value= \$ 20,000,000\\\\Interest\,rate\,(i) = 6\% = 0.06\\\\Time\,period = n = 5\,years\\\\FV(due) = A[\dfrac{(1+r)^{n}- 1} {r}](1 + r)\\\\= 20,000,000 = A[\dfrac{(1+0.06)^{5} - 1 } {0.06}](1 + 0.06)\\\\= 20,000,000 = A\times 5.98\\\\=\$\,3,344,481[/tex]
Hence, the amount of the annual deposit is equal to $3,344,481.
To learn more about Future value of annuity, refer to the link:
https://brainly.com/question/5303391
