Question

You put $200 into an account earning 6% interest compounded yearly.

Write a rule to model the situation. Your answer should not include spaces and be formatted like: y=3(4)^x


Based on your equation, when will the account be worth $2500? Round your answer to the nearest hundredths place and do not include labels. Ex. 3.14

Answer 1

43.35 years

Explanation:

From the above question, we are to find Time t for compound interest

The formula is given as :

t = ln(A/P) / n[ln(1 + r/n)]

A = $2500

P = Principal = $200

R = 6%

n = Compounding frequency = 1

First, convert R as a percent to r as a decimal

r = R/100

r = 6/100

r = 0.06 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(2,500.00/200.00) / ( 1 × [ln(1 + 0.06/1)] )

t = ln(2,500.00/200.00) / ( 1 × [ln(1 + 0.06)] )

t = 43.346 years

Approximately = 43.35 years