Question

Situation: Holly wants to save money for an emergency. Holly invests $800 in an account that pays an interest rate of 4%. A = P(1 + r)¹ P = amount of money invested r = interest rate percentage in decimal form How many years will it take for the account to reach $1,600? Round your answer to the nearest hundredth. Enter the correct answer. DONE​

Answer 1

t = 74.897 years

(about 74 years 11 months)

Explanation:

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

r = R/100

r = 4/100

r = 0.04 per year,

Then, solve the equation for t

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

t = ln(16,000.00/800.00) / ( 365 × [ln(1 + 0.04/365)] )

t = ln(16,000.00/800.00) / ( 365 × [ln(1 + 0.00010958904109589)] )

t = 74.897 years

Summary:

The time required to get a total amount of $16,000.00 with compoundeded interest on a principal of $800.00 at an interest rate of 4% per year and compounded 365 times per year is 74.897 years.

(about 74 years 11 months)

Since it wasn't stated howmany times the interest is compunded I took the value of once a year.