Financial Investment Calculations Explained

• How much has Astro accumulated by investing RM1,500 annually at an 8% compounded annual return for 12 years?
• What is the current value of Dellamin's mutual fund, considering he invested RM1,000 quarterly for 5 years with an 11% compounded quarterly return?
• How much lump sum should Stevence deposit today to withdraw RM3,000 annually for 5 years at an 8% compounded annual return?
• How much should Lucas invest today at 9.5% annual interest compound to have RM80,000 in 4 years for her son's wedding day?
• How much has Briotta accumulated by investing RM150 monthly for 20 years with an 11% annual return compounded monthly? And how much would she need to invest with a 10% return to achieve the same accumulation?

Astro's Accumulated Investment:

Astro has been investing RM1,500 annually for 12 years at an 8% compounded annual return. To calculate the accumulated amount, we can use the compound interest formula:

Amount = P(1 + r)^t

Where:
P = RM1,500 (annual investment)
r = 8% or 0.08 (annual interest rate)
t = 12 (number of years)

Plugging the values into the formula:

Amount = RM1,500(1 + 0.08)^12 = RM27,875.63

Therefore, Astro has accumulated approximately RM27,875.63 over 12 years.

Dellamin's Mutual Fund Value:

Dellamin invested RM1,000 quarterly for 5 years with an 11% compounded quarterly return. We can use the compound interest formula to find the current value of the mutual fund:

Amount = P(1 + (r/n))^(n x t)

Where:
P = RM1,000 (quarterly investment)
r = 11% or 0.11 (annual interest rate compounded quarterly)
t = 5 years
n = 4 (quarterly compounding)

Plugging the values into the formula:

Amount = RM1,000(1 + (0.11/4))^(4 x 5) = RM71,289.18

Therefore, the current value of Dellamin's mutual fund is RM71,289.18.

Stevence's Lump Sum Deposit:

To calculate the lump sum Stevence should deposit today to withdraw RM3,000 annually for 5 years at an 8% compounded annual return, we use the present value of an annuity formula:

PV = PMT [(1 - (1 + r)^-n) / r]

Where:
PV = Present Value (lump sum)
PMT = Payment per period (RM3,000 annually)
r = 8% or 0.08 (annual interest rate)
n = 5 years

Plugging the values into the formula:

PV = RM3,000 [(1 - (1 + 0.08)^-5) / 0.08] = RM11,443.13

Stevence should deposit approximately RM11,443.13 today to meet the withdrawals for the next 5 years.

Lucas's Investment For Her Son's Wedding:

To have RM80,000 in 4 years at an annual interest rate of 9.5% compounded annually, we calculate the present value of the future amount:

Present Value = Future Value / (1 + r)^t

Where:
Future Value = RM80,000
r = 9.5% or 0.095 (annual interest rate)
t = 4 years

Plugging the values into the formula:

Present Value = RM80,000 / (1 + 0.095)^4 = RM59,013.80

Lucas should invest approximately RM59,013.80 today at 9.5% annual interest to have RM80,000 in 4 years for her son's wedding.

Briotta's Accumulated Investment & Payment Adjustment:

For a monthly investment of RM150 for 20 years with an 11% annual return compounded monthly, we calculate the accumulated amount:

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

Where:
P = RM150 (monthly investment)
r = 11% or 0.11 (annual interest rate compounded monthly)
t = 20 years
n = 12 (monthly compounding)

Plugging the values into the formula:

Amount = RM150(1 + 0.11/12)^(12 x 20) = RM153,798.85

Therefore, Briotta has accumulated approximately RM153,798.85 over 20 years.

If Briotta could only earn 10% with monthly compounding, we recalculate the monthly payment amount:

Amount = RM150(1 + 0.10/12)^(12 x 20) = RM130,971.82

For Briotta to have the same accumulated amount with a 10% return, she would need to adjust her monthly payments to approximately RM129.48.