Question

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

Answer 1

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

$1.6141= (1+ \frac{0.022}{n}) ^{22n}$

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

The answer is yearly.