Question

Holly wants to save money for an emergency. Holly invests 1,500 in an account that pays an interest rate of 6.75%. How many years will it take for the account to reach 7300? Round your answer to the nearest hundredth.

Answer 1

The formula is
A=p (1+r)^t
A future value 7300
P present value 1500
R interest rate 0.0675
T time?
7300=1500 (1+0.0675)^t
Solve for t
Divide both sides by 1500
7300/1500=1.0675^t
Take the log for both sides
Log (7300/1500)=t×log (1.0675)
Divide both sides by log (1.0675)
T=log(7,300÷1,500)÷log(1.0675)
T=24.2 years round your answer to get 24 years

Hope it helps!

Answer 2

Although the problem didn't mention it, I guess this is a compound interest, if so, then:

A= P(1+i%)ⁿ , where P is the original capital, i% = interest and n= number of years

7300 = 1500(1 + 0.0675)ⁿ

7300/1500 = (1.0675)ⁿ

4.86666 = (1,0675)ⁿ

log(4.86666)= n.log(1.0675)
0.687231 = n(0.028367)

n = 0.687231 / 0.028367

n = 24.23 years