The correct statement is that Susan's monthly payment for a personal loan which is to be paid off in three years will be $143.3. So, the correct from the given choices is not given above.
The computation of monthly payment can be done by calculating the annuity and then dividing it by the number of months of the duration of payment of such loan.
Calculation of monthly payment
- Putting the given values into the formula for compounded annuity, the values obtained will be as,
- [tex]\rm Compounded\ Annuity= Principal(1+\dfrac{r}{n})^n^t\\\\\rm Compounded\ Annuity= 3500(1+\dfrac{0.13}{12})^1^2^ x ^3\\\\\\\rm Compounded\ Annuity= \$5158.60[/tex]
- Now dividing the total compounded annuity by number of months which is given as 36 months will be calculated as,
- [tex]\rm Monthly\ Payment = \dfrac{Annuity}{Period}\\\\\\\rm Monthly\ Payment = \dfrac{5158.60}{36}[/tex]
- So, the monthly payment will be,
- [tex]\rm Monthly\ Payment = \$143.29[/tex]
Hence, the correct option is not given above and the monthly compounded payment on a personal loan of $3500 for a period of 36 months will be $143.3.
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