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Sophie deposited money into an account in which interest is compounded semiannually at a rate of 3.7%. She made no other deposits or withdrawals and the total amount in her account after 15 years was $12,158.10. How much did she deposit?

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Sagot :

Fieryanswererftidn

$7,015.11

  • total money accrued : $12,158.10
  • years :  15 years
  • rate of interest : 3.7%
  • deposited : A

Depth meanings:

  • P is deposited money
  • semiannually : 2 times in a year
  • A is received or acquired money
  • t is time in years
  • r is rate in percentage

[tex]\sf P = \dfrac{A} { (1 + \dfrac{r}{n})^{nt}}[/tex]

[tex]\rightarrow \sf P = \dfrac{12,158.10} { (1 + \dfrac{3.7\%}{2})^{(2)(15)}}[/tex]

[tex]\rightarrow \sf P = \dfrac{12,158.10} { (1 + \dfrac{0.037}{2})^{(2)(15)}}[/tex]

[tex]\rightarrow \sf P = 7015.113646[/tex]

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