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A debt of
$10000.00 with interest at
8% compounded quarterly is to be repaid by equal payments at the end of every three months for two years.
a) Calculate the size of the monthly payments.
b) Construct an amortization table.
c) Calculate the outstanding balance after three payments.

A debt of $\$ 10000.00$ with interest at $8 \%$ compounded quarterly is to be repaid by equal payments at the end of every three months for two years. $\newline$ a) Calculate the size of the monthly payments. $\newline$ b) Construct an amortization table. $\newline$ c) Calculate the outstanding balance after three payments.

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Compound interest

Full solution

Q. A debt of

\$ 10000.00

with interest at

8 \%

compounded quarterly is to be repaid by equal payments at the end of every three months for two years.

\newline

a) Calculate the size of the monthly payments.

\newline

b) Construct an amortization table.

\newline

c) Calculate the outstanding balance after three payments.

Calculate Total Number of Payments: Next, we need to calculate the total number of payments. Since payments are made every three months and the debt is to be repaid over two years, there will be $2$ years $*$ $4$ quarters per year $=$ $8$ payments.
Use Present Value Formula: Now, we use the formula for the present value of an annuity to find the payment amount. The formula is $P = \frac{r \cdot PV}{1 - (1 + r)^{-n}}$ , where $P$ is the payment, $r$ is the quarterly interest rate, $PV$ is the present value of the loan, and $n$ is the number of payments. $P = \frac{0.02 \cdot 10000}{1 - (1 + 0.02)^{-8}}$
Calculate Payment Amount: Let's calculate the payment amount. $\newline$ P = $(0.02 \times 10000) / (1 - (1 + 0.02)^{-8})$ $\newline$ P = $(200) / (1 - (1.02)^{-8})$ $\newline$ P = $(200) / (1 - 1.02^{-8})$ $\newline$ P = $(200) / (1 - 0.8535)$ $\newline$ P = $200 / 0.1465$ $\newline$ P = $\$1365.53$

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