Question

A principal of $3900 is invested at 8.5% interest, compounded annually. How many years will it take to accumulate $7000 or more in the account? (Use thecalculator provided if necessary.)Write the smallest possible whole number answer.yearsXS?

Answer 1

The formula for calculating compound interest is expressed as

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

where

A is the amount after t years

t is the number of years

r is the interest rate

n is the number of compounding periods in a year

P is the principal or initial amount

From the information given,

P = 3900

r = 8.5/100 = 0.085

A = 7000

n = 1 because it was compunded once in a year

By substituting these values into the formula,

7000 = 3900(1 + 0.085/1)^1 * t

7000/3900 = 1.085^t

Take the natural log of both sides. We have

ln(7000/3900) = ln 1.085^t = tln1.085

t = ln(7000/3900) /ln 1.085

t = 7.17

Thus, the answer is

7 years