Question

the formula A=P(1+r)^2 gives the amount A in dollars that P dollars will grow to in 2 years at interest rate r (where r is given as a decimal),using compound interest .What interest rate will cause $5000 to grow to 5512.50 in 2 years

Answer 1

`A=P(1+r)^2\\\\A=\$5512.50;\ P=\$5000;\ r=?\\\\subtitute:\\\\5000(1+r)^2=5512.50\ \ \ \ |divide\ both\ sides\ by\ 5000\\\\(1+r)^2=1.1025\ \ \ \ |square\ root\ of\ both\ sides\\\\√((1+r)^2)=√(1.1025)\\\\1+r=1.05\ \ \ |subtract\ 1\ from\ both\ sides\\\\r=0.05\\\\0.05\cdot100\%=5\%\\\\Answer:\boxed{5\%}`