2.5 years required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Step-by-step explanation:
The given is,
Initial investment - $5000
Future amount - $6000
Interest rate - 7.5% (compounded quarterly)
Step:1
Formula to calculate the Future amount with compound interest,
...................................(1)
Where, F - Future amount
P - Initial amount
r - Rate of interest
n - No. of compounding in a year
t - Time period
From given,
F = $6000
P = $5000
r = 7.5%
n = 4 (compounded quarterly)
Equation (1) becomes,
Take log on both sides,
Substitute log values,
0.07918 = 4(t) (0.0080676)
= (t) (0.0322705)
= 2.45
t ≅ 2.5 years
Result:
2.5 years required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.