RM65000 will be invested for 6 years 9 months. if the investment will be offered 5% compounded semi annualy for the first 2 years, 6% compounded monthly for the next 18 months and 7% compounded daily for the rest of the period ,find the future value of this investment.
65000(1+.05/2)^(2*2)*(1+.06/12)^18*(1+.07/360)^1170 = 98534.95
To find the future value of the investment, we need to calculate the compounded interest for each period and then sum them up.
First, let's calculate the future value for the first 2 years, where the interest is compounded semiannually at a rate of 5%.
Step 1: Calculate the number of compounding periods:
Number of semiannual periods = 2 years * 2 = 4 periods
Step 2: Calculate the interest rate per period:
Interest rate per period = 5% / 2 = 2.5%
Step 3: Calculate the future value for the first 2 years:
Future value for the first 2 years = RM65000 * (1 + 2.5%)^4
Next, let's calculate the future value for the next 18 months, where the interest is compounded monthly at a rate of 6%.
Step 1: Calculate the number of compounding periods:
Number of monthly periods = 18 months * 12 = 216 periods
Step 2: Calculate the interest rate per period:
Interest rate per period = 6% / 12 = 0.5%
Step 3: Calculate the future value for the next 18 months:
Future value for the next 18 months = RM65000 * (1 + 0.5%)^216
Finally, let's calculate the future value for the remaining period, where the interest is compounded daily at a rate of 7%.
Step 1: Calculate the number of compounding periods:
Number of daily periods = (6 years * 365 days) - ((2 years * 365 days) + (18 months * 30 days))
Step 2: Calculate the interest rate per period:
Interest rate per period = 7% / 365
Step 3: Calculate the future value for the remaining period:
Future value for the remaining period = RM65000 * (1 + 7%)^(number of daily periods)
Now, sum up all the future values for each period to find the total future value of the investment.
Total future value = Future value for the first 2 years + Future value for the next 18 months + Future value for the remaining period
Please note that the calculations might take some time and it's recommended to use a financial calculator or software to get the precise value.
RM65000 will be invested for 6 years 9 months. if the investment will be offered 5% compounded semi annualy for the first 2 years, 6% compounded monthly for the next 18 months and 7% compounded daily for the rest of the period ,find the future value of this investment.
To find the future value of an investment, we can break down the time period and calculate the future value for each sub-period. Then, we can add up the future values to get the total future value of the investment.
First, let's calculate the future value for each sub-period:
1. The first 2 years: The investment is compounded semi-annually at a rate of 5%. Since there are 2 compounding periods per year, there will be a total of 4 compounding periods for the first 2 years. The formula to calculate the future value is:
FV = P(1 + r/n)^(nt)
where FV is the future value, P is the principal amount, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
FV = 65000 * (1 + 0.05/2)^(2*4)
FV = 65000 * (1 + 0.025)^8
FV = 65000 * (1.025)^8
FV = 65000 * 1.21063
FV ≈ 78,699.92
So, the future value for the first 2 years is approximately RM78,699.92.
2. The next 18 months: The investment is compounded monthly at a rate of 6%. Since there are 12 compounding periods per year, there will be a total of 18/12 = 1.5 years or 18 compounding periods for the next 18 months. The formula to calculate the future value is:
FV = P(1 + r/n)^(nt)
FV = 65000 * (1 + 0.06/12)^(12*1.5)
FV = 65000 * (1 + 0.005)^18
FV = 65000 * (1.005)^18
FV = 65000 * 1.09424
FV ≈ 71,120.61
So, the future value for the next 18 months is approximately RM71,120.61.
3. The remaining period (rest of the 6 years 9 months): The investment is compounded daily at a rate of 7%. The formula to calculate the future value is:
FV = P(1 + r/n)^(nt)
Here, since the investment is compounded daily, n is 365 (number of compounding periods per year) and t is 6.75 years.
FV = 65000 * (1 + 0.07/365)^(365*6.75)
FV = 65000 * (1 + 0.00019181)^2463.75
FV = 65000 * 1.74355
FV ≈ 113,250.79
So, the future value for the remaining period is approximately RM113,250.79.
Finally, we can add up the future values for each sub-period to get the total future value of the investment:
Total future value = Future value for the first 2 years + Future value for the next 18 months + Future value for the remaining period
Total future value = RM78,699.92 + RM71,120.61 + RM113,250.79
Total future value ≈ RM262,071.32
Therefore, the total future value of the investment is approximately RM262,071.32.