Question

If you open an account that compounds quarterly in 2020. In what year will it double the starting amount if it has an APR of 3.2%

Answer 1

Answer:

It will double in the year 2063

Step-by-step explanation:

Let the amount deposited be $x, when it doubles, the amount becomes $2x

we can use the compound interest formula to know when this will happen

The compound interest formula is as follows;

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

In this question,

A is the amount which is 2 times the principal and this is $2x

P is called the principal and it is the amount deposited which is $x

r is the interest rate which is 3.2% = 3.2/100 = 0.032

n is the number of times compounding takes place per year which is quarterly which equals to 4

t is the number of years which we want to calculate.

Substituting all these into the equation, we have;

2x = x(1+0.032/4)^4t

divide through by x

2 = (1+ 0.008)^4t

2 = (1.008)^4t

we use logarithm here

Take log of both sides

log 2 = log (1.008)^2t

log 2 = 2t log 1.008

2t = log 2/log 1.008

2t = 86.98

t = 86.98/2

t =43.49 which is 43 years approximately

Thus the year the money will double will be 2020 + 43 years = 2063