Question

Find the interest rate for a ​$4000 deposit accumulating to ​$5234.58​, compounded quarterly for 9 years

Answer 1

Interest rate = 3%

Step-by-step solution:

The formula to find the amount for the principal P, after n years with annual rate of interest r% compounded quarterly is:

`A=P(1+(r)/(4) )^(4n)`

Here, P = 4000, A = 5234.58 and n = 9

Therefore,

`5234.58=4000(1+(r)/(4) )^(4(9))`

`(5234.58)/(4000) = (1+(r)/(4) )^(36)`

`1.308645 = (1+(r)/(4) )^(36)`

`1+(r)/(4) =1.308645 ^{(1)/(36) }`

`1+(r)/(4) =1.0075`

`(r)/(4) =1.0075-1`

= 0.0075

r = 0.0075 × 4 = 0.03

= 3%