1. Salem plans to deposit $2200 every 6 months for 15 years to save for his son's higher education. The rate of return will be 4% compounded semi-annually for the first 5 years and 8% compounded semi-annually for the subsequent 10 years. Calculate the future value of this ordinary simple annuity, IF HE STOPS payment AFTER 5 YEARS. *
2. You miss the 8th to 12th payments of a loan. The loan payments are $519.27 each month and the interest rate is 8.45% compounded monthly. How much are you behind in your payments on the day that you miss the 12th payment? *

 

a.

Semiannual interest rate for the first 5 years=4%/2=2%

Number of semiannual payments in first 5 years=2*5=10

Semiannual deposit=$2,200

The formula for future value of an ordinary annuity is found below:

FV=semiannual deposit*(1+r)^n-1/r

FV=future value of first 5 years semiannual deposits which is unknown

semiannual deposit=$2,000

n=10( as above)

FV=2200*(1+2%)^10-1/2%

FV=2200*(1.02)^10-1/2%

FV=2200*( 1.21899442-1)/2%

FV=2200*0.21899442/2%

FV= $24,089.39 (FUTURE VALUE AFTER 5 YEARS)

Note that the FV in year 5 would still be in the account for the next 10 years earning 4% semiannually(8%/2)

FV=PV*(1+r)^n

PV=$24,089.39( This is future value in year 0 but present value in year 5 when this computation would take place)

r=4% semiannually

n=number of semiannual compounding in 10 years=10*2=20

FV=$24,089.39*(1+4%)^20=$52,782.82 

b.

The total number of missed payments is 5 ( 8th,9th,10th,11th and 12th)

amount of each payment=$519.27

monthly interest rate=8.45%/12= 0.00704167

The amount by which the borrower is behind is the future value of the 5 missed payments which comprises of the amounts and the interest that have accrued on them as computed below:

FV=monthly payment*(1+r)^n-1/r

FV=$519.27*(1+0.00704167)^5-1/0.00704167

FV=$519.27*(1.00704167)^5-1/0.00704167

FV=$519.27* (1.03570768795379-1)/0.00704167

FV=$519.27* 0.03570768795379/0.00704167

FV= $2,633.17