Rob has a balance of 1695$ in his bank account The account pays 2.9% interest per year, compounded annually. The compound interest formula is A=P(1+i)^n
A=future value\P=principal/i+interest rate/n=number of payments
rods balance will reach 3000$ after how many years?
1696(1.029)^n = 3000
1.029^n = 1.769
n = log1.769/log1.029 = 19.95
or abut 20 years
To find out how many years it will take for Rob's balance to reach $3000, we can use the compound interest formula A = P(1 + i)^n, where:
A = future value ($3000 in this case)
P = principal (initial balance of $1695)
i = interest rate per year (2.9% or 0.029 as a decimal)
n = number of years
We need to rearrange the formula to solve for n. Here's how we can do it:
1. Divide both sides of the equation by P:
(A / P) = (1 + i)^n
2. Take the logarithm of both sides of the equation to isolate n:
log(A / P) = log(1 + i)^n
3. Using logarithm properties, we can move the exponent in front of the logarithm:
n * log(1 + i) = log(A / P)
4. Finally, divide both sides of the equation by log(1 + i) to solve for n:
n = log(A / P) / log(1 + i)
Now, let's calculate the value of n for Rob's situation:
n = log(3000 / 1695) / log(1 + 0.029)
Using a calculator, we can evaluate the logarithms and find the value of n.