You want to buy a new car that costs 45,000. You have 34,897 in your account that has been saved already. The account earns 6% continuous interest. If you leave the account alone, how many years will it take for the money to grow to the needed amount?

Solution

Y o u w an t t o b u y a n e w c a r t ha t cos t s 45, 000. Y o u ha v e 34, 897 in yo u r a cco u n t t ha t ha s b ee n s a v e d a l re a d y . T h e a cco u n t e a r n s 6% co n t in u o u s in t eres t . I f yo u l e a v e t h e a cco u n t a l o n e, h o w man y ye a rs w i ll i t t ak e f or t h e m o n ey t o g ro w t o t h e n ee d e d am o u n t ?

Time : 4.24

Solution steps

Translate the problem into an equation:

45000 = 34897 e^{0.06 t}

Solve for

t, 45000 = 34897 e^{0.06 t} : t = 4.24

Time : 4.24