how much time will be needed for $21,000 to grow to $22,629.23 if deposited at 3% compounded quarterly

Question

how much time will be needed for $21,000 to grow to $22,629.23 if deposited at 3% compounded quarterly

Answer 1

general formula for compound interest is

A=P(1+r/n)^nt

where n=number of compounding periods per year =4

r = interest rate 3%

t = years

here's a slightly different problem with 20 instead of 21 thousand investment

P = starting investment= 20,000

A = ending Amount= 22,629.23

22,629.23 = 20,000(1+.03/4)^4t

solve for t, use a calculator with log functions

22629.23/20000=(1.0075)^4t

log_1.0075(1.1314615)=4t

4t= ln1.1314615/ln1,0075

t = .12351/.03=about 4.117 years

= about 4 years and 1 month

for $21,000 solve the same way

22629.23=21000(1.0075)^4t

solve for t