Question

To find how many years it will take for $250.00 deposited at the end of each quarter to amount to $11,453.40 at 6% compounded quarterly, you can enter the following in the financial calculator and find the number of years: P/Y = = C/Y 1/4 = PV = Choose... PMT = FV = Choose... CPT N = Choose... which rounds up to • quarterly payments so, the number of years is Choose...

Answer 1

P/Y = 4 = C/Y

I/Y = 4

PV = 0

PMT = -250

FV = 11453.40

CPT N = 35.132

Which rounds up to 35 quarterly payments

So, the number of years = 35/4 = 8.75 years

Formula to solve n manually,

e.

n = ln [(FV _n x i/PMT) + 1]/ln (1+i)

Explanation:

FV _n = PMT x [(1+i) ⁿ - 1/i]

[(1+i) ⁿ - 1/i] = FV _n / PMT

(1+i) ⁿ – 1 = (FV _n / PMT) x i or FV _n x i/ PMT

(1+i) ⁿ = (FV _n x i/ PMT) + 1

Taking log of both sides,

n x ln (1+i)= ln [(FV _n x i/ PMT) + 1]

n = ln [(FV _n x i/ PMT) + 1]/ ln (1+i)