# If you have \$1,150,000 in cash, how long will it take to accumulate \$2,000,000 in cash with the interest being at 5 percent per annum.

durbanville | Certified Educator

Please always remember to distinguish between simple and compound interest in financial questions as it does make a difference.

Take care to never round off too sound.

You will note here how it takes longer for the simple interest to accumulate than the compound interest as follows.

Use the formulae :

A = P (1 + in) (simple interest)

A = P (1 + i) ^n (compound interest)

when A is the future amount (ie \$2 000 000)

P is the present amount (ie \$1 150 000)

and the interest (i) in this case is 5% (that is 0, 05).

We are looking for the number of years (n)

Simple:     2 000 000 = 1 150 000(1 + 0,05n)

2 000 000/ 1 150 000 = 1 + 0,05n

1,739130435 - 1 = 0,05n

0,0739130435 / 0.05 = n

n = 14,78 years

Compound: 2 000 000 = 1 150 000 (1 + 0,05) ^n

2 000 000 / 1 150 000 = ( 1 + 0,05) ^n

log 1,739130435  = n log 1, 05

log 1,739130435 / log 1,05 = n

n = 11,34 years