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jeka57 [31]
2 years ago
11

Omar wants to open an account for his grandchildren that he hopes will have

Mathematics
1 answer:
olga_2 [115]2 years ago
4 0

Using compound interest, it is found that he must deposit $56,389.

Compound interest:

A(t) = P(1 + \frac{r}{n})^{nt}

  • A(t) is the amount of money after t years.  
  • P is the principal(the initial sum of money).  
  • r is the interest rate(as a decimal value).  
  • n is the number of times that interest is compounded per year.  
  • t is the time in years for which the money is invested or borrowed.

In this problem:

  • Hopes to have $80,000 in 20 years, thus t = 20, A(t) = 80000.
  • Interest rate of 1.75%, thus r = 0.0175.
  • Compounding monthly, thus n = 12
  • The investment is of P, for which we have to solve.

Then:

A(t) = P(1 + \frac{r}{n})^{nt}

80000 = P(1 + \frac{0.0175}{12})^{12(20)}

P = \frac{80000}{(1 + \frac{0.0175}{12})^{12(20)}}

P = 56389

He must deposit $56,389.

A similar problem is given at brainly.com/question/25263233

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