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Answer :
It will take approximately 6.97 years for a sum of RM12,000 to grow to RM15,000 at a nominal rate of 8% per year compounded monthly.
(a) The nominal rate compounded monthly can be calculated by multiplying the monthly interest rate by the number of compounding periods in a year. In this case, the credit card company charges 1.5% per month, so the nominal rate compounded monthly is:
Nominal rate compounded monthly = 1.5% * 12 = 18%
(b) The effective rate takes into account the compounding effect over a year and can be calculated using the formula:
Effective rate = (1 + r/n)^n - 1
Where r is the nominal rate and n is the number of compounding periods in a year. In this case, the nominal rate compounded monthly is 18% and the number of compounding periods is 12.
Effective rate = (1 + 18%/12)^12 - 1 ≈ 19.56%
To find out how long it will take for RM500 to grow to RM700 at a nominal rate of 8% compounded quarterly, we can use the formula for compound interest:
FV = PV * (1 + r/n)^(n*t)
Where FV is the future value, PV is the present value, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.
In this case, the present value (PV) is RM500, the future value (FV) is RM700, the interest rate (r) is 8%, and the number of compounding periods per year (n) is 4 (quarterly compounding).
RM700 = RM500 * (1 + 8%/4)^(4*t)
Simplifying the equation:
1.4 = (1 + 0.02)^(4*t)
Taking the logarithm of both sides:
log(1.4) = log(1.02)^(4*t)
Using logarithmic properties, we can rearrange the equation to solve for t:
4*t = log(1.4) / log(1.02)
t = (log(1.4) / log(1.02)) / 4 ≈ 3.58
Therefore, it will take approximately 3.58 years for RM500 to grow to RM700 at a nominal rate of 8% compounded quarterly.
To determine how many years it will take for a sum of RM12,000 to grow to RM15,000 at a nominal rate of 8% per year compounded monthly, we can use the same formula for compound interest:
FV = PV * (1 + r/n)^(n*t)
In this case, the present value (PV) is RM12,000, the future value (FV) is RM15,000, the interest rate (r) is 8%, and the number of compounding periods per year (n) is 12 (monthly compounding).
RM15,000 = RM12,000 * (1 + 8%/12)^(12*t)
Simplifying the equation:
1.25 = (1 + 0.0067)^(12*t)
Taking the logarithm of both sides:
log(1.25) = log(1.0067)^(12*t)
Rearranging the equation to solve for t:
12*t = log(1.25) / log(1.0067)
t = (log(1.25) / log(1.0067)) / 12 ≈ 6.97
Therefore, it will take approximately 6.97 years for a sum of RM12,000 to grow to RM15,000 at a nominal rate of 8% per year compounded monthly.
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