Given an interest rate of 6.25% compounded annually, how much would you accumulate if you started with $3,250 and then contributed $1,950 per year (at the end of each year) for 13 years?
Is this correct? Calculate each FV and sum?
PV1 = 3,250 i = 6.25% N = 13 FV =
PV2 = 1,950 i = 6.25% N = 12 FV =
PV3 = 1,950 i = 6.25% N = 11 FV =
PV4 = 1,950 i = 6.25% N = 10 FV =
PV5 = 1,950 i = 6.25% N = 9 FV =
PV6 = 1,950 i = 6.25% N = 8 FV =
PV7 = 1,950 i = 6.25% N = 7 FV =
PV8 = 1,950 i = 6.25% N = 6 FV =
PV9 = 1,950 i = 6.25% N = 5 FV =
PV10 = 1,950 i = 6.25% N = 4 FV =
PV11 = 1,950 i = 6.25% N = 3 FV =
PV12 = 1,950 i = 6.25% N = 2 FV =
PV13 = 1,950 i = 6.25% N = 1 FV =
To calculate the future value (FV) of each contribution and the total accumulated amount, you can use the formula for compound interest:
FV = P(1 + r)^n
Where:
- FV is the future value
- P is the principal amount (initial investment)
- r is the annual interest rate (expressed as a decimal)
- n is the number of compounding periods
In this case, you have an initial investment (PV1) of $3,250 and annual contributions of $1,950 per year (PV2 to PV13) for 13 years. The interest rate is 6.25%, which needs to be converted to a decimal (0.0625).
Using the formula, we can calculate each FV:
FV1 = 3,250(1 + 0.0625)^13
FV2 = 1,950(1 + 0.0625)^12
FV3 = 1,950(1 + 0.0625)^11
FV4 = 1,950(1 + 0.0625)^10
FV5 = 1,950(1 + 0.0625)^9
FV6 = 1,950(1 + 0.0625)^8
FV7 = 1,950(1 + 0.0625)^7
FV8 = 1,950(1 + 0.0625)^6
FV9 = 1,950(1 + 0.0625)^5
FV10 = 1,950(1 + 0.0625)^4
FV11 = 1,950(1 + 0.0625)^3
FV12 = 1,950(1 + 0.0625)^2
FV13 = 1,950(1 + 0.0625)^1
To find the total accumulated amount, you can simply add up all the individual FV values:
Total Accumulated Amount = FV1 + FV2 + FV3 + ... + FV13
Now you can compute the individual FV values and the total accumulated amount.
To calculate the future value (FV) for each cash flow, you can use the formula:
FV = PV * (1 + i)^n
where PV is the present value, i is the interest rate, and n is the number of years.
Let's calculate the FV for each contribution:
PV1 = $3,250, i = 6.25%, N = 13
FV1 = $3,250 * (1 + 0.0625)^13 = $6,282.02
PV2 = $1,950, i = 6.25%, N = 12
FV2 = $1,950 * (1 + 0.0625)^12 = $3,882.53
PV3 = $1,950, i = 6.25%, N = 11
FV3 = $1,950 * (1 + 0.0625)^11 = $3,516.13
PV4 = $1,950, i = 6.25%, N = 10
FV4 = $1,950 * (1 + 0.0625)^10 = $3,171.89
PV5 = $1,950, i = 6.25%, N = 9
FV5 = $1,950 * (1 + 0.0625)^9 = $2,847.71
PV6 = $1,950, i = 6.25%, N = 8
FV6 = $1,950 * (1 + 0.0625)^8 = $2,541.28
PV7 = $1,950, i = 6.25%, N = 7
FV7 = $1,950 * (1 + 0.0625)^7 = $2,250.15
PV8 = $1,950, i = 6.25%, N = 6
FV8 = $1,950 * (1 + 0.0625)^6 = $1,972.55
PV9 = $1,950, i = 6.25%, N = 5
FV9 = $1,950 * (1 + 0.0625)^5 = $1,706.18
PV10 = $1,950, i = 6.25%, N = 4
FV10 = $1,950 * (1 + 0.0625)^4 = $1,448.78
PV11 = $1,950, i = 6.25%, N = 3
FV11 = $1,950 * (1 + 0.0625)^3 = $1,198.99
PV12 = $1,950, i = 6.25%, N = 2
FV12 = $1,950 * (1 + 0.0625)^2 = $956.47
PV13 = $1,950, i = 6.25%, N = 1
FV13 = $1,950 * (1 + 0.0625)^1 = $2,072.81
To determine the total accumulated amount, you need to sum up all the FV values:
Total Accumulated Amount = FV1 + FV2 + FV3 + ... + FV13
Total Accumulated Amount = $6,282.02 + $3,882.53 + $3,516.13 + $3,171.89 + $2,847.71 + $2,541.28 + $2,250.15 + $1,972.55 + $1,706.18 + $1,448.78 + $1,198.99 + $956.47 + $2,072.81
Total Accumulated Amount ≈ $34,271.30