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Misha deposited $3,725 into a savings account 22 years ago. The account has an interest rate of 2.2% and the balance is currently $6,012.37. How often does the interest compound?

daily
monthly
quarterly
annually

Respuesta :

stevekimaz
The compounding equation is [tex]A=P(1+ \frac{r}{n}) ^{nt} [/tex]. So
 
[tex] 6012.37 = 3725(1+ \frac{0.022}{n}) ^{22n} [/tex]    Divide by 3725

[tex] 1.6141= (1+ \frac{0.022}{n}) ^{22n} [/tex]

Daily      = [tex](1+ \frac{0.022}{365}) ^{22*365} [/tex]
              = [tex](1.000060274) ^{8030} [/tex]
              = 1.6225
Monthly  = [tex](1+ \frac{0.022}{12}) ^{22*12} [/tex]
              = [tex](1.0018333) ^{264} [/tex]
              = 1.6218
Quarter  = [tex](1+ \frac{0.022}{4}) ^{22*4} [/tex]
              = [tex](1.0055) ^{88} [/tex]
              = 1.6204
Yearly  = [tex](1+ \frac{0.022}{1}) ^{22*1} [/tex]
              = [tex](1.022) ^{22} [/tex]
              = 1.6141

The answer is yearly.





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