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Question 85625: Problem #1
Student Loans Student borrowers now have more options to
choose from when selecting repayment plans.* The standard
plan repays the loan in 10 years with equal monthly payments.
The extended plan allows from 12 to 30 years to repay the loan.
A student borrows $35,000 at 7.43% compounded monthly.
Find the monthly payment and total interest paid under the
standard plan.
Problem #2
Inheritance Sandi Goldstein has inherited $25,000 from
her grandfather’s estate. She deposits the money in an
account offering 6% interest compounded annually. She
wants to make equal annual withdrawals from the account
so that the money (principal and interest) lasts exactly
8 years.
a. Find the amount of each withdrawal.
b. Find the amount of each withdrawal if the money must
last 12 years.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The standard plan repays the loan in 10 years with equal monthly payments.
A student borrows $35,000 at 7.43% compounded monthly.
Find the monthly payment and total interest paid under the
standard plan.
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Formula:
Loan Balance = (original amount)(1+r)^n-[(payment amt)/i][(1+i)^n-1]
i is the interest for each payment period; n is # of payments
You want the loan balance to be zero.
0 = 35000(1+.0743/12)^(10*12) - [P/(0.0743/12)][(1+(0.0743/12)^120 -1]
0 = 35000(1.006191667)^120 - [P/0.006191667][1.006191667^120 - 1]
0 = 35000 - [P/0.006191667][1.0974225777}
0=73409.79 -P*177.24
P = $414.18 (monthly payment made for 120 months
Total Interest = 120*414.18-35000= $14,701.44
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Inheritance Sandi Goldstein has inherited $25,000 from
her grandfather’s estate. She deposits the money in an
account offering 6% interest compounded annually. She
wants to make equal annual withdrawals from the account
so that the money (principal and interest) lasts exactly
8 years.
a. Find the amount of each withdrawal.
Same formula as above. By the way you can find formulas using Google
and searching on "investment formulas".
0 = 25000(1.06)^8-[P/0.06][(1.06)^8 - 1]
Solve for P.
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b. Find the amount of each withdrawal if the money must
last 12 years.
Let n=12 and solve for P.
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Cheers,
Stan H.
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