aris saved rm25,000 at 8% compounded monthly,two years later,he withdrew rm14000 from the savings, find the amount left in the account
To find the amount left in the account, we need to calculate the new balance after the withdrawal.
Firstly, we calculate the interest earned over the two-year period using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount after interest
P = the principal amount (initial savings)
r = annual interest rate (8% as a decimal = 0.08)
n = number of times interest is compounded per year (monthly = 12)
t = time in years (2)
A = 25000(1 + 0.08/12)^(12*2)
A = 25000(1 + 0.00666666667)^(24)
A ≈ 25000(1.00666666667)^24
A ≈ 25000(1.177191940048)
A ≈ 29429.80
The amount after two years would be approximately RM29,429.80.
Next, we subtract the amount withdrawn from the balance after two years:
Remaining balance = 29429.80 - 14000
Remaining balance = 15429.80
The amount left in the account after the withdrawal is approximately RM15,429.80.
To find the amount left in the account after Aris withdrew RM14,000, we need to calculate the future value of his initial savings after two years of compounding and then subtract the amount he withdrew.
First, let's calculate the future value (FV) of Aris' initial savings after two years.
We will use the formula for compound interest:
FV = P * (1 + r/n)^(nt)
Where:
FV = Future Value
P = Principal amount (initial savings)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case:
P = RM25,000
r = 8% or 0.08 (in decimal form)
n = 12 (compounded monthly)
t = 2
FV = 25,000 * (1 + 0.08/12)^(12*2)
FV = 25,000 * (1.00667)^(24)
Calculating the value:
FV = 25,000 * 1.16532
FV = RM 29,133
So, after two years of compounding at an 8% interest rate, the future value of Aris' initial savings is RM29,133.
Next, we subtract the amount he withdrew from the future value to find the amount left in the account:
Amount left = FV - Amount Withdrawn
Amount left = RM29,133 - RM14,000
Amount left = RM15,133
Therefore, the amount left in the account is RM15,133.
To find the amount left in the account, we need to calculate the final balance after two years and then subtract the amount withdrawn.
First, let's calculate the final balance after two years using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final balance
P = Principal amount (Initial savings)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
Given:
P = RM25,000
r = 8% = 0.08 (converted to decimal form)
n = 12 (compounded monthly)
t = 2 years
A = 25000(1 + 0.08/12)^(12*2)
Now, let's calculate A:
A = 25000(1 + 0.00667)^(24)
A = 25000(1.00667)^(24)
Use a calculator or spreadsheet to compute 1.00667^24 and multiply it by 25000 to find the final balance after two years. Let's denote this balance as F.
F = 25000 * 1.00667^24
Next, subtract the amount withdrawn (RM14,000) from the final balance:
Amount left in the account = F - RM14,000
Calculate F and subtract RM14,000 from it to find the amount left in the account.