Question

Fly your family to the slopes by investing

in $25/week. Adds up to $7380 in 5 years.
What is the annual interest rate? Please answer answer step by step in full detail

Answer 1

The annual rate of interest is 2.56%

Explanation:

Given as :

Principal Amount investing every week = $25

Principal Amount investing in 5 years = $25 × 5 × 52 = p = $6500

The Amount adds after 5 years = A = $7380

Time period = t = 5 years

Let annual rate of interest = r %

Now, According to question

Amount after 5 years = Principal ×
`(1+(\textrm rate)/(100))^(\textrm time)`

Or, A = p ×
`(1+(\textrm r)/(100))^(\textrm t)`

Or, $7380 = $6500 ×
`(1+(\textrm r)/(100))^(\textrm 5)`

Or,
`(7380)/(6500)` =
`(1+(\textrm r)/(100))^(\textrm 5)`

Or, 1.135 =
`(1+(\textrm r)/(100))^(\textrm 5)`

Or,
`(1.135)^{(1)/(5)}` = 1 +
`(r)/(100)`

Or, 1.0256 = 1 +
`(r)/(100)`

Or, 1.0256 - 1 =
`(r)/(100)`

Or, 0.0256 =
`(r)/(100)`

∴ r = 0.0256 × 100

i.e r = 2.56

So, The rate of interest = r = 2.56

Hence, The annual rate of interest is 2.56% Answer