Find the time required for an investment of 5000 dollars to grow to 8700 dollars at an interest rate of 7.5 percent per year, compounded quarterly. Your answer is t= years. You may enter the exact value or round to 2 decimal places.

Solution

F in d t h e t im e re q u i re d f or an in v es t m e n t o f 5000 d o ll a rs t o g ro w t o 8700 d o ll a rs a t an in t eres t r a t e o f 7.5 p erce n t p er ye a r, co m p o u n d e d q u a r t er l y . Y o u r an s w er i s t = ye a rs . Y o u ma y e n t er t h e e x a c t v a l u e or ro u n d t o 2 d ec ima l pl a ces .

Time : 7.45

Solution steps

Translate the problem into an equation:

8700 = 5000 (1 + \frac{0.075}{4})^{4 t}

Solve for

t, 8700 = 5000 (1 + \frac{0.075}{4})^{4 t} : t = 7.45415 \dots

Time : 7.45415 \dots

Round

7.45415 \dots

to the nearest 2 decimal places:

7.45

Time : 7.45