Question

Algebraically manipulating the formula FV = P + Prt, find the simple interest rate it would take to double (2 times) the initial deposit of $7,000 for 8 years.

A. 10%
B. 11%
C. 12.5%
D. 9.5%
E. None of these

Answer 1

To double a $7,000 deposit in 8 years using simple interest, the formula derives a rate of 0.125, which equates to 12.5%. Therefore, the answer is option C: 12.5%.

Step-by-step explanation:

To find the simple interest rate needed to double a $7,000 deposit over 8 years, we can use the simple interest formula. The future value (FV) needed is $14,000, since that is double the initial deposit. We can set up the equation as follows:

2P = P + Prt

This simplifies to P = Prt, because we want to double the principal (P), which means the FV becomes 2P and then we subtract P from both sides. Dividing both sides by (P * t) gives us:

1/t = r

With an initial deposit (P) of $7,000 and a time (t) of 8 years, we get:

1/8 = r

r = 0.125 or 12.5%

Therefore, the simple interest rate required to double the investment in 8 years is 12.5%.