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+ (r)/(n)) ^(nt)`. So


`6012.37 = 3725(1+ (0.022)/(n)) ^(22n)` Divide by 3725


`1.6141= (1+ (0.022)/(n)) ^(22n)`

Daily =
`(1+ (0.022)/(365)) ^(22*365)`
=
`(1.000060274) ^(8030)`
= 1.6225
Monthly =
`(1+ (0.022)/(12)) ^(22*12)`
=
`(1.0018333) ^(264)`
= 1.6218
Quarter =
`(1+ (0.022)/(4)) ^(22*4)`
=
`(1.0055) ^(88)`
= 1.6204
Yearly =
`(1+ (0.022)/(1)) ^(22*1)`
=
`(1.022) ^(22)`
= 1.6141

The answer is yearly.