time required word problem

Question

Find the time required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly. 

Answer 1

general formula is

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

where P = investment

A = ending Amount

r= interest rate

n = number of compounding periods per year

t = years

P=5000

A=6000

r=7.5% = .075

n=4

plug in the numbers, solve for t

6000=5000(1+.075/4)^4t

6000/5000= (1.01875)^4t

6/5 =1.2= 1.01875^4t

1.2 = 1.01875^4t

take logs of both sides, to the base 1.01875

log_1.018751.2 =4t

ln1.2/ln1.01875 ₌ 4t

t= ln1.2/4ln1.01875

t = 9.328337553

t= about 9.3 years

for $5000 to grow to $6000,

at 7.5% interest compounded quarterly