The total lifetime cost of all the loans is $31336.8
Further Explanation:
Present Value: It is the current value of a future cash flow or streams of cash flow calculated at given a specific rate of return. The present value the as:
[tex]${\text{Present Value (PV)= A}}\,{\text{\times}}\,\,\frac{{\left({{\text{1}}-\left({\frac{{\text{1}}}{{{{\left( {{\text{1 + r}}} \right)}^{\text{n}}}}}}\right)}\right)}}{{\text{r}}}$[/tex]
Calculate the total lifetime cost of the loan:
[tex]\begin{aligned}\text{Total lifetime cost of loans}&=\text{Monthly cost of loans}\times\text{Total years}\times12\\&=\$261.14\times10\times12\\&=\$31,336.8\end{aligned}[/tex]
Thus, the total lifetime cost of all the loans is $31336.8
Working note 1:
Calculate the monthly payment:
[tex]\begin{aligned}A&=\$ 22,000\\r&=7.5\%\\n&=10\,{\text{years}}\\\\\end{aligned}[/tex]
Then,
[tex]\begin{aligned}PV&=A\times\dfrac{\left[1-\left(\dfrac{1}{(1+r)^{n}}\right)\right]}{r}\\&=\$22,000\times\dfrac{\left[1-\left(\dfrac{1}{\left(1+\dfrac{7.5}{12}\right)^{120}}\right)\right]}{\dfrac{7.5}{12}}\\&=\$261.14\end{aligned}[/tex]
Thus, the total amount of monthly payment is $261.14
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Answer details:
Grade: High School
Subject: Financial Management
Chapter: Time Value of Money
Keywords: At the, beginning, of each, of, her, four, years, in college, Miranda, took, out, a new, Stafford, loan, Each, loan, had, a principal, of $5,500, an interest, rate, of, 7.5%, compounded, monthly, and, a duration, often, year,. Miranda, paid, off, each loan, by making, constant, monthly payments, starting, with, when, she, graduated, All, of the loans, were subsidized, What is the total, lifetime, cost, for Miranda, to pay, off her, 4 loans.
