Question

Que: How many years will it take to acquire the 1.5 million if you only earn 6% and have 50k now and put in 12k per year?

a. 54

b. 33

c. 40

d. 38

Answer 1

Future value of annuity= payment per period * [(1+i)^n - 1]/i  

i = interest rate per period

n = number of periods

Present value = Future value/(1+i)^n

i = interest rate per period

n= number of periods

=>

50000 * (1+6%)^n + 12000 * [(1+6%)^n - 1]/6% = 1500000

=>

50000*0.06* (1+6%)^n + 12000*(1+6)^n - 12000 = 1500000 * 6%

=>

3000 * 1.06^n + 12000*1.06^n = 102000

=>

15000 * 1.06^n = 102000

=>

1.06^n = 6.8

=>

n = ln(6.8)/ln(1.06)

= 32.90 years

= 33 years

choose b)