Find the sum to be invested now at 6% compounded monthly so as to accumulate RM8 888 in three years
P(1 + 0.06/12)^(12*3) = 8888
Find the amount to be invested now at 6% compounded monthly so as to accumulate RM8,000 in 3 years.
To find the sum to be invested now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (RM8,888 in this case)
P = Principal amount (to be determined)
r = Annual interest rate (6% or 0.06)
n = Number of times interest is compounded per year (monthly, so n = 12)
t = Number of years (3 years)
Now let's plug in the values and solve for P:
8888 = P(1 + 0.06/12)^(12 * 3)
Dividing both sides by P:
8888/P = (1 + 0.06/12)^(36)
Taking the 36th root of both sides to isolate (1 + 0.06/12) on the right-hand side:
(8888/P)^(1/36) = 1 + 0.06/12
Subtracting 1 from both sides:
(8888/P)^(1/36) - 1 = 0.06/12
Simplifying:
(8888/P)^(1/36) - 1 = 0.005
Now, let's solve for (8888/P)^(1/36):
(8888/P)^(1/36) = 1 + 0.005
Taking both sides to the power of 36:
8888/P = (1 + 0.005)^36
Simplifying:
8888/P = 1.221
Multiplying both sides by P:
8888 = 1.221P
Dividing both sides by 1.221:
P = 8888 / 1.221
P ≈ RM7,277.76
Therefore, approximately RM7,277.76 should be invested now at 6% compounded monthly to accumulate RM8,888 in three years.
To find the sum to be invested now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount we want to accumulate
P = the initial principal (the sum to be invested)
r = the annual interest rate (in decimal form)
n = the number of compounding periods per year
t = the number of years
In this case, we want the final amount (A) to be RM8,888 in three years. The interest rate (r) is 6% per year. The compounding is monthly, so there are 12 compounding periods per year (n = 12). The time period (t) is three years.
Substituting the given values into the formula:
8888 = P(1 + 0.06/12)^(12*3)
Now, let's solve this equation for P, the sum to be invested:
P = 8888 / (1 + 0.06/12)^(12*3)
To calculate this, we can use a calculator or spreadsheet. The result will give us the sum that needs to be invested now to accumulate RM8,888 in three years at a 6% interest rate compounded monthly.