Deposit and saving

For how long will the deposit of € 2,000 increase at an interest rate of 4.6% p. a. at 2500 €? (Ideally calculate without logarithms)

Correct answer:

n =  5

Step-by-step explanation:

q=100%+4.6%=1+1004.6=1.046 a=2000 E b=2500 E  a1=a q=2000 1.046=2092 a2=a1 q=2092 1.046=2188.232 a3=a2 q=2188.232 1.0462288.8907 a4=a3 q=2288.8907 1.0462394.1796 a5=a4 q=2394.1796 1.0462504.3119  a5>2500 eur  n=5   Verifying Solution:  b=a qx lnb/a=xlnq  x=ln(b/a)/lnq=ln(2500/2000)/ln1.0464.9617

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