How much must you deposit now on January 12017 to have a balance of br 10000 on December 31 2025 ? Interest is compounded at 8 % annual rate .
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = final amount (in this case, br 10000)
P = principal amount (what we need to find)
r = annual interest rate (8% or 0.08)
n = number of times compounded per year (assume annually, so n=1)
t = time in years (8 years)
Substituting the given values, we have:
10000 = P(1 + 0.08/1)^(1*8)
10000 = P(1.08)^8
10000/1.08^8 = P
P = 4393.45
Therefore, you need to deposit br 4393.45 now on January 1, 2017 to have a balance of br 10000 on December 31, 2025.
How large must each annual payment be for a br 100000 loan to be repaid in equal installment at the end of each of the next 5 years . The interest rate is 10% compounded annually.
We can use the formula for the present value of an annuity:
PV = PMT * [(1 - (1 / (1 + r)^n)) / r]
where:
PV = present value of the loan (br 100000)
PMT = annual payment (what we need to find)
r = annual interest rate (10% or 0.1)
n = number of years (5)
Substituting the given values, we have:
100000 = PMT * [(1 - (1 / (1 + 0.1)^5)) / 0.1]
100000 = PMT * [(1 - (1 / 1.61051)) / 0.1]
100000 = PMT * [4.868]
PMT = 100000 / 4.868
Therefore, each annual payment should be br 20,533.51 to repay the br 100000 loan in equal installments at the end of each of the next 5 years with an interest rate of 10% compounded annually.
To calculate the amount you need to deposit now to have a balance of BR 10,000 on December 31, 2025, with an 8% annual interest rate compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value (BR 10,000)
P = the principal amount (the amount to be deposited)
r = the annual interest rate (8% or 0.08)
n = the number of times interest is compounded per year (annually)
t = the number of years (from January 1, 2017 to December 31, 2025)
Solving the equation for P:
BR 10,000 = P(1 + 0.08/1)^(1 * 8)
BR 10,000 = P(1.08)^8
Next, we can solve for P:
BR 10,000 / (1.08)^8 = P
Using a calculator or a spreadsheet:
BR 10,000 / 1.71775 = P
P ≈ BR 5,822.72
Therefore, you need to deposit approximately BR 5,822.72 now on January 1, 2017, to have a balance of BR 10,000 on December 31, 2025.