Question

A vacation property valued at $29,900 was bought for 300 payments of $235 due at the end of every month.

What nominal annual rate of interest compounded quarterly was​ charged?

The nominal annual rate of interest is ______compounded quarterly.

Answer 1

Instalment = Loan / PVAF(r%, n)

PVAF (r%, n) = Loan / Instalment

= $ 29900 / 300

= 99.67

The Rate at which PVAF for 300 periods is 99.6667, the same is int rate per quarter.

PVAF(0.95%,300 ) = 99.09

PVAF(0.90%,300) = 103.55

Required Rate = 0.90% + [ (103.55 - 99.67 ) / ( 103.55 - 99.09 ) ] * 0.05%

= 0.90% + [ 3.88 / 4.46 ] * 0.05%

= 0.90% + [ 0.87 * 0.05% ]

= 0.90% + 0.04%

= 0.94%

Nominal Rate = 0.94% * 12 / 3

= 3.76%

Pls do rate, if the answer is correct and Comment, if any further assistance is required