Peter invests $12500 for 5 years at 12 percent per annum,compounded monthly foe the first two years, and 14 percent per annum compounded simiannually for the next three years. How much will Peter receive after five years?
Solve it as two problems.
Principal, P = $12500
1. 2 years at 12% p.a. compounded monthly
2. 3 years at 14% p.a. compunded semi-annually.
1.
monthly interest = 12%/12 = 1%
R=1+0.01=1.01
n=2/(1/12)=24
Amount after 2 years,
A2=PR^24 = $12500*1.01^24 = $15871.68
2.
semi-annual interest = 14%/2 = 7%
R = 1+0.07 = 1.07
n=3/(1/0.5)=6
Final amount,
A = A2*R^6 = $15,871.68*1.07^6 = $23,819.12
To calculate the amount Peter will receive after five years, we need to use the formula for compound interest. The formula is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount Peter will receive
P = the principal amount (initial investment) which is $12500
r = the annual interest rate in decimal form: 12% = 0.12 for the first two years and 14% = 0.14 for the next three years
n = the number of times the interest is compounded per year: monthly = 12 times for the first two years, and semi-annually = 2 times for the next three years
t = the number of years: 5 years
First, let's calculate the amount Peter will receive after two years using monthly compounding:
A1 = P(1 + r/n)^(nt)
A1 = 12500(1 + 0.12/12)^(12*2)
A1 = 12500(1 + 0.01)^24
A1 = 12500(1.01)^24
A1 ≈ 14699.245
Now, let's calculate the amount Peter will receive after the next three years using semi-annual compounding:
A2 = A1(1 + r/n)^(nt)
A2 = 14699.245(1 + 0.14/2)^(2*3)
A2 = 14699.245(1 + 0.07)^6
A2 = 14699.245(1.07)^6
A2 ≈ 21568.584
Finally, let's calculate the amount Peter will receive after five years:
A = A2 = 21568.584
Therefore, Peter will receive approximately $21,568.58 after five years.