Question

Damon is saving up money for a down payment on a condominium. He currently has $4818$ 4818, but knows he can get a loan at a lower interest rate if he can put down $5381$ 5381. If he invests the $4818$ 4818 in an account that earns 5.6%5.6% annually, compounded continuously, how long will it take Damon to accumulate the $5381$ 5381? Round your answer to two decimal places, if necessary.

Answer 1

Time t = 2.03 years

Explanation:

The standard formula for compound interest is given as;

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

For n = 1

A = P(1+r)^(t)

Making t the subject of formula;

t = ln(A/P)÷ln(1+r) .....2

Where;

A = final amount/value

P = initial amount/value (principal)

r = rate yearly

n = number of times compounded yearly.

t = time of investment in years

For this case;

A = $5381

P = $4818

t = ?

n = 1

r = 5.6% = 0.056

Using equation 2;

t = ln(5381/4818)÷ln(1+0.056)

t = 2.028243842925

t = 2.03 years (to two decimal place)