Question
A 21 year old who invests K17.50 a day until retiring at the age of 65 at a 5 per cent average annual investment return can be a millionaire.
At the age of 30, the required daily savings amount almost doubles. At age 40 the amount quadruples .
How much is his total investment show calculation?
At the age of 30, the required daily savings amount almost doubles. At age 40 the amount quadruples .
How much is his total investment show calculation?
Answers
GPT-4o mini
To determine how much the total investment will be by the age of 65, we can calculate it in three phases based on the ages mentioned (21, 30, and 40), and then extend this till retirement age.
### Definitions
- Daily Investment: K17.50
- Annual Return Rate: 5%
- Total Investment Duration: 44 years (from age 21 to 65)
### Phases of Investment
1. **From Age 21 to 30 (9 Years)**
- Daily Investment: K17.50
- Total Days: 9 years = 9 * 365 = 3285 days
- Total Investment at this point:
\[
\text{Total Investment} = K17.50 \times 3285 = K57,487.50
\]
2. **From Age 30 to 40 (10 Years)**
- Daily Investment doubles: K35.00
- Total Days: 10 years = 10 * 365 = 3650 days
- Total Investment at this point:
\[
\text{Total Investment} = K35.00 \times 3650 = K127,750.00
\]
3. **From Age 40 to 65 (25 Years)**
- Daily Investment quadruples: K70.00
- Total Days: 25 years = 25 * 365 = 9125 days
- Total Investment at this point:
\[
\text{Total Investment} = K70.00 \times 9125 = K638,750.00
\]
### Total Investment Without Interest
Now, let's sum up the total investment contributions (without considering interest yet):
\[
\text{Total Investment (Principal)} = 57,487.50 + 127,750 + 638,750 = K824,987.50
\]
### Calculating Future Value with Compounding Interest
To calculate the future value of these investments when compounded annually at 5% interest, we need to calculate the future value of each investment period.
1. **Future Value of Contribution from Age 21 to 30 after reaching 65**:
- Duration until retirement: 65 - 30 = 35 years
\[
FV = P \times (1 + r)^n = 57,487.50 \times (1 + 0.05)^{35}
\]
2. **Future Value of Contribution from Age 30 to 40 after reaching 65**:
- Duration until retirement: 65 - 40 = 25 years
\[
FV = 127,750 \times (1 + 0.05)^{25}
\]
3. **Future Value of Contribution from Age 40 to 65**:
- Duration until retirement: 0 years (this amount is already at retirement)
\[
FV = K638,750
\]
### Calculating Each Future Value
Using a calculator:
1. FV from age 21 to 30:
\[
FV = 57,487.50 \times (1.05)^{35} \approx 57,487.50 \times 5.227 = K300,162.82
\]
2. FV from age 30 to 40:
\[
FV = 127,750 \times (1.05)^{25} \approx 127,750 \times 3.386 = K432,589.50
\]
3. FV from age 40 to 65:
\[
FV = K638,750
\]
### Total Future Value at Age 65
\[
\text{Total Future Value} = 300,162.82 + 432,589.50 + 638,750 = K1,371,502.32
\]
Thus, the total amount at age 65, accounting for investment contributions and growth through compounding interest, would be approximately K1,371,502.32.
### Definitions
- Daily Investment: K17.50
- Annual Return Rate: 5%
- Total Investment Duration: 44 years (from age 21 to 65)
### Phases of Investment
1. **From Age 21 to 30 (9 Years)**
- Daily Investment: K17.50
- Total Days: 9 years = 9 * 365 = 3285 days
- Total Investment at this point:
\[
\text{Total Investment} = K17.50 \times 3285 = K57,487.50
\]
2. **From Age 30 to 40 (10 Years)**
- Daily Investment doubles: K35.00
- Total Days: 10 years = 10 * 365 = 3650 days
- Total Investment at this point:
\[
\text{Total Investment} = K35.00 \times 3650 = K127,750.00
\]
3. **From Age 40 to 65 (25 Years)**
- Daily Investment quadruples: K70.00
- Total Days: 25 years = 25 * 365 = 9125 days
- Total Investment at this point:
\[
\text{Total Investment} = K70.00 \times 9125 = K638,750.00
\]
### Total Investment Without Interest
Now, let's sum up the total investment contributions (without considering interest yet):
\[
\text{Total Investment (Principal)} = 57,487.50 + 127,750 + 638,750 = K824,987.50
\]
### Calculating Future Value with Compounding Interest
To calculate the future value of these investments when compounded annually at 5% interest, we need to calculate the future value of each investment period.
1. **Future Value of Contribution from Age 21 to 30 after reaching 65**:
- Duration until retirement: 65 - 30 = 35 years
\[
FV = P \times (1 + r)^n = 57,487.50 \times (1 + 0.05)^{35}
\]
2. **Future Value of Contribution from Age 30 to 40 after reaching 65**:
- Duration until retirement: 65 - 40 = 25 years
\[
FV = 127,750 \times (1 + 0.05)^{25}
\]
3. **Future Value of Contribution from Age 40 to 65**:
- Duration until retirement: 0 years (this amount is already at retirement)
\[
FV = K638,750
\]
### Calculating Each Future Value
Using a calculator:
1. FV from age 21 to 30:
\[
FV = 57,487.50 \times (1.05)^{35} \approx 57,487.50 \times 5.227 = K300,162.82
\]
2. FV from age 30 to 40:
\[
FV = 127,750 \times (1.05)^{25} \approx 127,750 \times 3.386 = K432,589.50
\]
3. FV from age 40 to 65:
\[
FV = K638,750
\]
### Total Future Value at Age 65
\[
\text{Total Future Value} = 300,162.82 + 432,589.50 + 638,750 = K1,371,502.32
\]
Thus, the total amount at age 65, accounting for investment contributions and growth through compounding interest, would be approximately K1,371,502.32.