Saeed has taken a loan such that debts of $4000.00, $4500.00 and $5000.00 are due in one year, eighteen months and two years from now respectively. He won a lottery and would like to make a single payment now that would settle the debts if interest is 5.99% p.a. compounded quarterly.
A) $13 500.00
B) $12 324.59
C) $14 796.16
D) $13 079.58
E) $13 880.82

Question

Quizplus · Accepted Answer

Using the formula $A=P(1+\frac{r}{n})^{nt}$,
the future values of debts $4000, 4500$ and $5000$ become $4183.91, 4841.78$ and $5633.02$ respectively when the interest is compounded quarterly at 5.99%.

Thus, the total amount payable after the given time period is $14658.71$.

To settle these debts with a single payment, we need to find the present value of these debts now.

Using the formula $PV=\frac{FV}{(1+\frac{r}{n})^{nt}}$,

the present value of the debts becomes $3677.10, 4136.00$ and $4491.34$ respectively.

The sum of present values is $12304.44$.

Hence, the best option is B) $12 324.59$ as it is closest to $12304.44$.

Saeed Has Taken a Loan Such That Debts of $4000