Question

Assume a savings account offers a rate of return of 4% per year.

At 4% per year, how many full years will it take for $6,000 in savings to grow to $20,000?

(By full years, the question means you should round up to the nearest whole year and your answer should be an integer.)

Answer 1

Here formula of future value can be used

Future value = present value(1+r)^n

r = rate of interest = 4%

n = no of years = ?

Present value = 6000$

Future value = 20000$

20000 = 6000(1+4%)^n

20000 = 6000(1+0.04)^n

3.3333 = 1.04^n

Suppose n = 30

1.04^30 = 3.2434

now lets suppose n = 31

1.04^31 = 3.3731

Thus n is between 30 and 31. This can be found using interpolation method

n	1.04^n
30	3.2434
31	3.3731
1	0.1297
?	0.0899

=0.0899/0.1297

=0.6931

Thus n = 30+0.6931

= 30.6931 years

Thus 31 years