The amount you should deposit is $4709.18
Step-by-step explanation:
The formula for compound interest, including principal sum is
, where:
- A is the future value of the investment/loan, including interest
- P is the principal investment amount
- r is the annual interest rate in decimal
- n is the number of times that interest is compounded per unit t
- t is the time the money is invested or borrowed for
∵ You want to have $5000 in your savings account in 2 years
∴ A = 5000
∴ t = 2
∵ The account pays 3% annual interest, compounded monthly
∴ r = 3% = 3 ÷ 100 = 0.03
∴ n = 12 ⇒ compounded monthly
- Substitute these values in the formula above
∴ ![5000=P(1+\frac{0.03}{12})^{(12)(2)}](https://tex.z-dn.net/?f=5000%3DP%281%2B%5Cfrac%7B0.03%7D%7B12%7D%29%5E%7B%2812%29%282%29%7D)
∴ ![5000=P(1+0.0025)^{24}](https://tex.z-dn.net/?f=5000%3DP%281%2B0.0025%29%5E%7B24%7D)
∴ ![5000=P(1.0025)^{24}](https://tex.z-dn.net/?f=5000%3DP%281.0025%29%5E%7B24%7D)
- Divide both sides by ![(1.0025)^{24}](https://tex.z-dn.net/?f=%281.0025%29%5E%7B24%7D)
∴ P = 4709.18
The amount you should deposit is $4709.18
Learn more:
You can learn more about the compounded interest in brainly.com/question/2514241
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