Answer to Question #216737 in Financial Math for Kelly

Question #216737

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


1
Expert's answer
2021-07-14T10:12:30-0400

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

"r = \\frac{5.35}{100}\\\\\n\nr = 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)}\\\\\n4611 = 3470\\times(1.000146575)^{(365t)}\\\\\n\\frac{4611}{3470}=(1.000146575)^{(365t)}\\\\\n1.328818444=(1.000146575)^{(365t)}\\\\\nt=\\frac{ln(1.328818444)}{365ln(1.00014657)}\\\\t=5.31423659\n=5.3years"

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