Solve the problem.
-If $300,000 is to be saved over 25 years, how much should be deposited monthly if the investment earns 8% interest compounded monthly?
A) $315.45
B) $180.48
C) $260.87
D) $216.62

Question

Quizplus · Accepted Answer

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = Amount after time t
P = Principal (initial amount)
r = Annual interest rate as a decimal
n = Number of times the interest is compounded per year
t = Time in years

We can solve for P, which is the amount that needs to be deposited monthly:

P = (A / ((1 + r/n)^(nt))) / (12t)

We plug in the given values:

A = 300,000
r = 0.08
n = 12 (compounded monthly)
t = 25

P = (300,000 / ((1 + 0.08/12)^(12*25))) / (12*25)
P ≈ $315.45

Therefore, the best choice is A, depositing $315.45 monthly. We can use the formula for monthly payments on a savings plan with compound interest:

$PMT = \frac{PV\cdot r}{1-(1+r)^{-n}}

where:
PMT = monthly payment
PV = present value (amount to be saved)
r = monthly interest rate (8% divided by 12)
n = number of months (25 years times 12 months)

Plugging in the values:

PMT = \frac{300000\cdot 0.08/12}{1-(1+0.08/12)^{-(25\cdot 12)}}

PMT = 315.45

Therefore, the monthly deposit should be $315.45. The answer is (A).

Solve the Problem. -If $300,000 Is to Be Saved Over 25 Years, How