Answer to Question #216737 in Financial Math for Kelly

Question

Find the number of years needed for a $3,470 deposit to grow to $4,611 when interest is 5.35% compounded daily. 

Answer 1

First, convert R as a percent to r as a decimal

$r = \frac{5.35}{100}\\ r = 0.0535$ rate per year,

$A = P(1 +\frac{ r}{n})^{nt}$

A = Accrued amount,P is the Principal ,r is annual nominal interest rate as a decimal,n is number of compounding periods per unit of time and t time in decimal years

$4611 = 3470\times(1 + \frac{0.0535}{365})^{(365)(t)}\\ 4611 = 3470\times(1.000146575)^{(365t)}\\ \frac{4611}{3470}=(1.000146575)^{(365t)}\\ 1.328818444=(1.000146575)^{(365t)}\\ t=\frac{ln(1.328818444)}{365ln(1.00014657)}\\t=5.31423659 =5.3years$