The formula for a simple interest rate is I = PRT and Total Balance = P + I
The formula for compound interest is B = P × (1 + 〖r/n)〗^nt
Adam invests £55,000 at interest rate of 4% per annum
and if compounded, compounded yearly or monthly or weekly or daily or continuously ?
To calculate the interest and total balance for Adam's investment of £55,000 at an interest rate of 4% per annum, we will use the formula for simple interest and compound interest.
1. Simple Interest:
The formula for simple interest is I = PRT, where:
I = interest
P = principal amount
R = interest rate
T = time in years
Given that Adam invests £55,000 at an interest rate of 4% per annum, we can calculate the simple interest:
I = £55,000 × 0.04 × 1 (since the time is not specified in the question) = £2,200
To find the total balance, we use the formula Total Balance = P + I:
Total Balance = £55,000 + £2,200 = £57,200
Therefore, the interest for Adam's investment is £2,200, and the total balance is £57,200.
2. Compound Interest:
The formula for compound interest is B = P × (1 + r/n)^nt, where:
B = final balance
P = principal amount
r = interest rate
n = number of times interest is compounded per year
t = time in years
Given that Adam invests £55,000 at an interest rate of 4% per annum, we need to know the compounding period (n) and the time (t) in order to calculate the compound interest.
Please provide the compounding period (n) and the time (t) to proceed with calculating the compound interest.
To calculate the simple interest, we can use the formula I = PRT, where:
- I is the interest
- P is the principal (the initial investment)
- R is the interest rate
- T is the time period in years
For Adam's investment of £55,000 at an interest rate of 4% per annum, we can plug these values into the formula:
I = £55,000 × 0.04 × 1
Therefore, the simple interest earned in one year would be £2,200.
To calculate the total balance (including the principal and interest), we can use the formula Total Balance = P + I:
Total Balance = £55,000 + £2,200
Therefore, the total balance after one year would be £57,200.
Now, let's calculate the compound interest using the compound interest formula:
B = P × (1 + r/n)^(nt)
Where:
- B is the balance after time period t
- P is the principal
- r is the annual interest rate (in decimal form)
- n is the number of times the interest is compounded per year
- t is the time period in years
For Adam's investment of £55,000 at an interest rate of 4% per annum, let's assume the interest is compounded annually (n = 1). We can calculate the compound interest after 1 year (t = 1):
B = £55,000 × (1 + 0.04/1)^(1 × 1)
Simplifying the equation:
B = £55,000 × 1.04^1
Therefore, the balance after one year would be £57,200, which is the same as the total balance in the case of compound interest with annual compounding.
So, in this particular case, both the formulas for simple interest and compound interest give the same result.