Question

Suppose you invest $150 a month for 4 years into an account earning 6% compounded monthly. After 4 years, you leave the money, without making additional deposits, in the account for another 24 years. How much will you have in the end?

Answer 1

To calculate the amount you'll have in the end, we can break the problem into two parts. For the first four years of investing $150 a month, the future value is $9,719.38. For the remaining 24 years without making additional deposits, the future value is approximately $27,808.38.

Step-by-step explanation:

To calculate the amount you'll have in the end, we can break the problem into two parts: the first four years of investing $150 a month, and the remaining 24 years without making additional deposits.

For the first four years, we can calculate the future value of an annuity with monthly compounding using the formula:

FV = P * ((1 + r)^n - 1) / r

where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the number of months. In this case, P = $150, r = 0.06/12 = 0.005, and n = 4 * 12 = 48. Substituting these values into the formula, we get:

FV = 150 * ((1 + 0.005)^48 - 1) / 0.005 = $9,719.38

For the remaining 24 years, we can calculate the future value of a lump sum using the formula:

FV = P * (1 + r)^n

where FV is the future value, P is the initial investment, r is the monthly interest rate (0.06/12 = 0.005), and n is the number of months (24 * 12 = 288). Substituting these values into the formula, we get:

FV = 9,719.38 * (1 + 0.005)^288 = $27,808.38

So, in the end, you will have approximately $27,808.38.