Question

If you had a bank that offered 6.1% interest and compounded money 4 times a year, how many years would go by until you could turn $6000 into enough to buy a brand new car ($12,000)?

Answer 1

t = 11.45 years

Explanation:

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

A = future value = $12000

P = present value = $6000

n = number of periods = 4

r = interest rate = 6.1% = 0.061

t = number of years = ?

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

= log(12000/6000) / 4[log(1+0.061/4)]

= log(2) / 4[log(1 + 0.01525)]

= 0.3010 / 4[log(1.01525)]

= 0.3010 / 4(0.00657)

= 0.3010 / 0.02628

= 11.45 years